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HP 12C Platinum
Owner’s Handbook
and
Problem-Solving Guide
© Hewlett-Packard Company 2003
2
Introduction
About This Handbook
This HP 12C Platinum Owners Handbook and Problem-Solving Guide is
intended to help you get the most out of your investment in your HP 12C
Platinum Programmable Financial Calculator. Although the excitement of
acquiring this powerful financial tool may prompt you to set this handbook aside
and immediately begin “pressing buttons,” in the long run you’ll profit by
reading through this handbook and working through the examples it contains.
Following this introduction is a brief section called Making Financial
Calculations Easy—which shows you that your HP 12C Platinum does just that!
The remainder of this handbook is organized basically into three parts:
z Part I (sections 1 through 7) describes how to use the various financial,
mathematics, statistics, and other functions (except for programming)
provided in the calculator:
z Section 1 is about Getting Started. It tells you how to use the keyboard,
how to do simple arithmetic calculations and chain calculations, and
how to use the storage registers (“memories”).
z Section 2 tells you how to use the percentage and calendar functions.
z Section 3 tells you how to use the simple interest, compound interest,
and amortization functions.
z Section 4 tells you how to do discounted cash flow analysis, bond, and
depreciation calculations.
z Section 5 tells you about miscellaneous operating features such as
Continuous Memory, the display, and special function keys.
z Sections 6 and 7 tell you how to use the statistics, mathematics, and
number-alteration functions.
z Part II (sections 8 through 11) describe how to use the powerful
programming capabilities of the HP 12C Platinum.
z Part III (sections 12 through 16) give you step-by-step solutions to
specialized problems in real estate, lending, savings, investment analysis,
and bonds. Some of these solutions can be done manually, while others
involve running a program. Since the programmed solutions are both self-
contained and step-by-step, you can easily employ them even if you don’t
care to learn how to create your own programs. But if you do start to create
your own programs, look over the programs used in the solutions: they
contain examples of good programming techniques and practices.
Introduction 3
z The various appendices describe additional details of calculator operation
as well as warranty and service information.
z The Function Key Index and Programming Key Index at the back of the
handbook can be used as a handy page reference to the comprehensive
information inside the manual
Financial Calculations in the United Kingdom
The calculations for most financial problems in the United Kingdom are
identical to the calculations for those problems in the United States – which are
described in this handbook. Certain problems, however, require different
calculation methods in the United Kingdom than in the United States. Refer to
Appendix G for more information.
For More Solutions to Financial Problems
In addition to the specialized solutions found in Sections 12 through 16 of this
handbook, many more are available in the optional HP 12C Platinum Solutions
Handbook. Included are solutions to problems in lending, forecasting, pricing,
statistics, savings, investment analysis, personal finance, securities, Canadian
mortgages, learning curves in manufacturing, and queuing theory. The solutions
handbook is available from your authorized HP dealer.
5
Contents
Introduction ...................................................................................... 2
About This Handbook..................................................................................... 2
Financial Calculations in the United Kingdom ................................................ 3
For More Solutions to Financial Problems...................................................... 3
Part I: Problem Solving................................................15
Section 1: Getting Started................................................................... 16
Power On and Off......................................................................................... 16
Low-Power Indication ............................................................................. 16
The Keyboard ............................................................................................... 16
Keying in Numbers ................................................................................. 17
Digit Separators...................................................................................... 17
Negative Numbers.................................................................................. 17
Keying in Large Numbers ....................................................................... 18
The CLEAR Keys ................................................................................... 18
The RPN and ALG Keys......................................................................... 19
Simple Arithmetic Calculations in RPN Mode............................................... 19
Chain Calculations in RPN Mode ................................................................. 20
Storage Registers......................................................................................... 23
Storing and Recalling Numbers.............................................................. 24
Clearing Storage Registers .................................................................... 25
Storage Register Arithmetic.................................................................... 25
Section 2: Percentage and Calendar Functions............................ 27
Percentage Functions................................................................................... 27
Percentages ........................................................................................... 27
Net amount............................................................................................. 27
Percent Difference.................................................................................. 28
Percent of Total ...................................................................................... 29
Calendar Functions ...................................................................................... 30
Date Format............................................................................................ 30
Future or Past Dates .............................................................................. 31
Number of Days Between Dates ............................................................ 32
Section 3: Basic Financial Functions............................................... 34
The Financial Registers................................................................................ 34
Storing Numbers Into the Financial Registers........................................ 34
Displaying Numbers in the Financial Registers ...................................... 34
Clearing the Financial Registers............................................................. 34
Simple Interest Calculations ......................................................................... 35
Financial Calculations and the Cash Flow Diagram ..................................... 36
The Cash Flow Sign Convention ............................................................ 38
The Payment Mode ................................................................................ 38
Generalized Cash Flow Diagrams.......................................................... 39
6 Contents
Compound Interest Calculations .................................................................. 41
Specifying the Number of Compounding Periods and the Periodic
Interest Rate ........................................................................................... 41
Calculating the Number of Payments or Compounding Periods ............ 41
Calculating the Periodic and Annual Interest Rates ............................... 45
Calculating the Present Value ................................................................ 46
Calculating the Payment Amount ........................................................... 48
Calculating the Future Value .................................................................. 49
Odd-Period Calculations......................................................................... 51
Amortization.................................................................................................. 54
Section 4: Additional Financial Functions...................................... 58
Discounted Cash Flow Analysis: NPV and IRR............................................ 58
Calculating Net Present Value (NPV)..................................................... 59
Calculating Internal Rate of Return (IRR)............................................... 63
Reviewing Cash Flow Entries................................................................. 64
Changing Cash Flow Entries .................................................................. 66
Bond Calculations......................................................................................... 67
Bond Price.............................................................................................. 67
Bond Yield .............................................................................................. 68
Depreciation Calculations............................................................................. 68
Section 5: Additional Operating Features....................................... 70
Continuous Memory ..................................................................................... 70
The Display................................................................................................... 70
Status Indicators..................................................................................... 70
Number Display Formats........................................................................ 71
Scientific Notation Display Format.......................................................... 72
Special Displays ..................................................................................... 73
The
~ Key................................................................................................ 74
The
F Key ............................................................................................... 74
Arithmetic Calculations With Constants.................................................. 75
Recovering From Errors in Digit Entry.................................................... 75
Section 6: Statistics Functions .......................................................... 76
Accumulating Statistics................................................................................. 76
Correcting Accumulated Statistics................................................................ 77
Mean............................................................................................................. 77
Standard Deviation....................................................................................... 78
Linear Estimation.......................................................................................... 79
Weighted Mean ............................................................................................ 81
Section 7: Mathematics and Number-Alteration Functions ....... 82
One-Number Functions ................................................................................ 82
The Power Function ..................................................................................... 84
Contents 7
Part II: Programming....................................................85
Section 8: Programming Basics........................................................ 86
Why Use Programs? .................................................................................... 86
Creating a Program ...................................................................................... 86
Running a Program ...................................................................................... 87
Program Memory.......................................................................................... 88
Identifying Instructions in Program Lines................................................ 89
Displaying Program Lines....................................................................... 90
The
i000 Instruction and Program Line 000..................................... 91
Expanding Program Memory.................................................................. 91
Setting the Calculator to a Particular Program Line ............................... 93
Executing a Program One Line at a Time .................................................... 94
Interrupting Program Execution.................................................................... 95
Pausing During Program Execution ....................................................... 95
Stopping Program Execution.................................................................. 98
Section 9: Branching and Looping................................................. 101
Simple Branching ....................................................................................... 101
Looping....................................................................................................... 101
Conditional Branching ................................................................................ 104
Section 10: Program Editing............................................................. 110
Changing the Instruction in a Program Line ............................................... 110
Adding Instructions at the End of a Program.............................................. 111
Adding Instructions Within a Program ........................................................ 112
Adding Instructions by Replacement .................................................... 112
Adding Instructions by Branching ......................................................... 113
Section 11: Multiple Programs......................................................... 117
Storing Another Program............................................................................ 117
Running Another Program.......................................................................... 119
Part III: Solutions........................................................121
Section 12: Real Estate and Lending ............................................. 122
Annual Percentage Rate Calculations With Fees....................................... 122
Price of a Mortgage Traded at a Discount or Premium .............................. 124
Yield of a Mortgage Traded at a Discount or Premium .............................. 125
The Rent or Buy Decision........................................................................... 127
Deferred Annuities...................................................................................... 131
Section 13: Investment Analysis..................................................... 134
Partial-Year Depreciation ........................................................................... 134
Straight-Line Depreciation.................................................................... 134
Declining-Balance Depreciation ........................................................... 137
Sum-of-the-Years-Digits Depreciation.................................................. 139
Full- and Partial-Year Depreciation with Crossover.................................... 141
Excess Depreciation................................................................................... 145
Modified Internal Rate of Return................................................................. 145
8 Contents
Section 14: Leasing............................................................................ 148
Advance Payments..................................................................................... 148
Solving For Payment ............................................................................ 148
Solving for Yield.................................................................................... 150
Advance Payments With Residual ............................................................. 152
Solving for Payment ............................................................................. 152
Solving For Yield .................................................................................. 154
Section 15: Savings............................................................................ 156
Nominal Rate Converted to Effective Rate................................................. 156
Effective Rate Converted to Nominal Rate................................................. 157
Nominal Rate Converted to Continuous Effective Rate.............................. 158
Section 16: Bonds............................................................................... 159
30/360 Day Basis Bonds ............................................................................ 159
Annual Coupon Bonds................................................................................ 161
Appendixes ................................................................ 165
Appendix A: RPN and the Stack .................................................... 166
Getting Numbers Into the Stack: The \ Key ......................................... 167
Termination of Digit Entry ..................................................................... 168
Stack Lift............................................................................................... 168
Rearranging Numbers in the Stack ............................................................ 168
The
~ Key........................................................................................ 168
The
d Key.......................................................................................... 168
One-Number Functions and the Stack ....................................................... 169
Two-Number Functions and the Stack ....................................................... 169
Mathematics Functions......................................................................... 169
Percentage Functions........................................................................... 170
Calendar and Financial Functions.............................................................. 171
The LAST X Register and the
F KEY ................................................... 172
Chain Calculations in RPN Mode ............................................................... 172
Arithmetic Calculations with Constants ...................................................... 173
Appendix B: Algebraic Mode (ALG) .............................................. 175
Simple Arithmetic calculations in ALG mode.............................................. 175
Keying in Negative Numbers (
Þ)........................................................... 175
Chain Calculations in ALG mode................................................................ 176
Percentage Functions................................................................................. 176
Percent Difference................................................................................ 177
Percent of Total .................................................................................... 177
The Power Function ................................................................................... 178
Appendix C: More About L ......................................................... 179
Appendix D: Error Conditions ........................................................ 181
Error 0: Mathematics .................................................................................. 181
Error 1: Storage Register Overflow ............................................................ 181
Error 2: Statistics ........................................................................................ 182
Error 3: IRR ................................................................................................ 182
Contents 9
Error 4: Memory.......................................................................................... 182
Error 5: Compound Interest........................................................................ 182
Error 6: Storage Registers.......................................................................... 183
Error 7: IRR ................................................................................................ 183
Error 8: Calendar........................................................................................ 184
Error 9: Service........................................................................................... 184
Pr Error ....................................................................................................... 184
Appendix E: Formulas Used ............................................................ 185
Percentage ................................................................................................. 185
Interest........................................................................................................ 185
Simple Interest...................................................................................... 185
Compound Interest............................................................................... 185
Amortization................................................................................................ 186
Discounted Cash Flow Analysis ................................................................. 187
Net Present Value ................................................................................ 187
Internal Rate of Return ......................................................................... 187
Calendar..................................................................................................... 187
Actual Day Basis .................................................................................. 187
30/360 Day Basis ................................................................................. 188
Bonds ......................................................................................................... 188
Depreciation ............................................................................................... 189
Straight-Line Depreciation.................................................................... 189
Sum-of-the-Years-Digits Depreciation.................................................. 190
Declining-Balance Depreciation ........................................................... 190
Modified Internal Rate of Return................................................................. 190
Advance Payments..................................................................................... 191
Interest Rate Conversions .......................................................................... 191
Finite Compounding ............................................................................. 191
Continuous Compounding.................................................................... 191
Statistics ..................................................................................................... 191
Mean..................................................................................................... 191
Weighted Mean .................................................................................... 192
Linear Estimation.................................................................................. 192
Standard Deviation............................................................................... 192
Factorial................................................................................................ 192
The Rent or Buy Decision........................................................................... 193
Appendix F: Battery, Warranty, and Service Information ........ 195
Battery ........................................................................................................ 195
Low-Power Indication ................................................................................. 195
Installing a New Battery........................................................................ 195
Verifying Proper Operation (Self-Tests) ..................................................... 196
Warranty ..................................................................................................... 198
Service........................................................................................................ 200
Potential For Radio/Television Interference (for U.S.A. Only) .................... 201
Temperature Specifications........................................................................ 201
Noise Declaration ....................................................................................... 201
Regulation applying to The Netherlands .................................................... 202
10 Contents
Appendix G: United Kingdom Calculations ................................ 203
Mortgages................................................................................................... 203
Annual Percentage Rate (APR) Calculations ............................................. 203
Bond Calculations....................................................................................... 204
Function Key Index ..................................................................... 205
Programming Key Index ............................................................. 208
Subject Index ............................................................................... 211
11
Making Financial
Calculations Easy
Before you begin to read through this handbook, let’s take a look at how easy
financial calculations can be with your HP 12C Platinum. While working
through the examples below, don’t be concerned about learning how to use the
calculator; we’ll cover that thoroughly beginning with Section 1.
Example 1: Suppose you want to ensure that you can finance your daughters
college education 14 years from today. You expect that the cost will be about
$6,000 a year ($500 a month) for 4 years. Assume she will withdraw $500 at the
beginning of each month from a savings account. How much would you have to
deposit into the account when she enters college if the account pays 6% annual
interest compounded monthly?
This is an example of a compound interest calculation. All such problems
involve at least three of the following quantities:
z n: the number of compounding periods.
z i: the interest rate per compounding period.
z PC: the present value of a compounded amount.
z PMT: the periodic payment amount.
z FV: the future value of a compounded amount.
In this particular example:
z n is 4 years × 12 periods per year = 48 periods.
z i is 6% per year ÷ 12 periods per year = 0.5% per period.
z PV is the quantity to be calculated – the present value when the financial
transaction begins.
z PMT is $500.
z FV is zero, since by the time your daughter graduates she (hopefully!) will
not need any more money.
To begin, turn the calculator on by pressing the ; key. Then, press the keys
shown in the Keystrokes column below.
1
Note: A battery symbol ( ) shown in the upper-left corner of the
display when the calculator is on signifies that the available battery power
is nearly exhausted. To install new batteries, refer to Appendix F.
The calendar functions and nearly all of the financial functions take some
1.
If you are not familiar with the use of an HP calculator keyboard, refer to the description
on pages 16 and 17.
12 Making Financial Calculations Easy
time to produce an answer. (This is typically just a few seconds, but the
¼, !, L, and S functions could require a half-minute or more.)
During these calculations, the word running flashes in the display to let
you know that the calculator is running.
Example 2: We now need to determine how to accumulate the required deposit
by the time your daughter enters college 14 years from now. Let’s say that she
has a paid-up $5,000 insurance policy that pays 5.35% annually, compounded
semiannually. How much would it be worth by the time she enters college?
In this example, we need to calculate FV, the future value.
Example 3: The preceding example showed that the insurance policy will
provide about half the required amount. An additional amount must be set aside
to provide the balance (21,396.61 – 10,470.85 = 10,925.76). Suppose you make
monthly payments, beginning at the end of next month, into an account that pays
6% annually, compounded monthly. What payment amount would be required in
order to accumulate $10,925.75 in the 14 years remaining?
Keystrokes Display
fCLEARHf2
0.00
Clears previous data inside the
calculator and sets display to show
two decimal places.
4gA
48.00
Calculates and stores the number of
compounding periods.
6gC
0.50
Calculates and stores the periodic
interest rate.
500P
500.00
Stores periodic payment amount.
500.00
Sets payment mode to Begin.
$
–21,396.61
Amount required to be deposited.
a
a Don’t be concerned now about the minus sign in the display. That and other details will
be explained in Section 3.
Keystrokes (RPN mode) Display
fCLEARG
–21,396.61
Clears previous financial data
inside the calculator.
14\2§w
28.00
Calculates and stores the number of
compounding periods.
5.35\2
2.68
Calculates and stores the periodic
interest rate.
5000Þ$
–5000.00
Stores the present value of the
policy.
M
10,470.85
Value of policy in 14 years.
Making Financial Calculations Easy 13
Example 4: Suppose you cannot find a bank that currently offers an account
with 6% annual interest compounded monthly, but you can afford to make
$45.00 monthly payments. What is the minimum interest rate that will enable
you to accumulate the required amount?
In this problem, we do not need to clear the previous financial data inside the
calculator, since most of it is unchanged from the preceding example.
This is only a small sampling of the many financial calculations that can now be
done easily with your HP 12C Platinum. To begin learning about this powerful
financial took, just turn the page.
Keystrokes Display
fCLEARG
10,470.85
Clears previous financial data
inside the calculator.
14gA
168.00
Calculates and stores the number of
compounding periods.
6gC
0.50
Calculates and stores the periodic
interest rate.
10925.76M
10.925.76
Stores the future value required.
10.925.76
Sets payment mode to End.
P
–41.65
Monthly payment required.
Keystrokes Display
45ÞP
–45.00
Stores payment amount.
¼
0.42
Periodic interest rate.
12§
5.01
Annual interest rate.
Part I
Problem Solving
16
Section 1
Getting Started
Power On and Off
To begin using your HP 12C Platinum, press the ; key
1
. Pressing ; again
turns the calculator off. If not manually turned off, the calculator will turn off
automatically 8 to 17 minutes after it was last used.
Low-Power Indication
A battery symbol ( ) shown in the upper-left corner of the display when the
calculator is on signifies that the available battery power is nearly exhausted. To
replace the batteries, refer to Appendix F.
The Keyboard
Many keys on the HP 12C Platinum perform two or even three functions. The
primary function of a key is indicated by the characters printed in white on the
upper face of the key. The alternate function(s) of a key are indicated by the
characters printed in gold above the key and the characters printed in blue on the
lower face of the key. These alternate functions are specified by pressing the
appropriate prefix key before the function key.
:
Throughout this handbook, references to the operation of an alternate function
appear as only the function name in a box (for example, “The L function …”).
References to the selection of an alternate function appear preceded by the
1.
Note that the ; key is lower than the other keys to help prevent its being pressed
inadvertently.
z To specify the alternate function printed in
gold above a key, press the gold prefix key
(f), then press the function key.
z To specify the primary function printed on
the upper face of a key, press the key alone.
z To specify the alternate function printed in
blue on the lower face of a key, press the
blue prefix key (g), then press the
function key.
Section 1: Getting Started 17
appropriate prefix key (for example, “Pressing fL …”). References to the
functions shown on the keyboard in gold under the bracket labeled “CLEAR
appear throughout this handbook preceded by the word “CLEAR” (for example,
“The CLEAR H function …” or “Pressing fCLEARH …”).
If you press the f or g prefix key mistakenly, you can cancel it by pressing
fCLEAR X. This can also be pressed to cancel the ?, :, and i
keys. (These keys are “prefix” keys in the sense that other keys must be pressed
after them in order to execute the corresponding function.) Since the X key is
also used to display the mantissa (all 10 digits) of a displayed number, the
mantissa of the number in the display will appear for a moment after the X
key is released.
Pressing the f or g prefix key turns on the corresponding status indicator – f
or g – in the display. Each indicator turns off when you press a function key
(executing an alternate function of that key), another prefix key, or
fCLEAR X.
Keying in Numbers
To key a number into the calculator, press the digit keys in sequence, just as if
you were writing the number on paper. A decimal point must be keyed in (using
the decimal point key) if it is part of the number unless it appears to the right of
the last digit.
Digit Separators
As a number is keyed in, each group of three digits to the left of the decimal
point is automatically separated in the display. When the calculator is first turned
on after coming from the factory – or after Continuous Memory is reset – the
decimal point in displayed numbers is a dot, and the separator between each
group of three digits is a comma. If you wish, you can set the calculator to
display a comma for the decimal point and a dot for the three-digit separator. To
do so, turn the calculator off, then press and hold down the . key while you
press ;. Doing so again sets the calculator to use the original digit separators
in the display.
Negative Numbers
To make a displayed number negative – either one that has just been keyed in or
one that has resulted from a calculation – simply press Þ (change sign). When
the display shows a negative number – that is, the number is preceded by a minus
sign – pressing Þ removes the minus sign from the display, making the
number positive.
18 Section 1: Getting Started
Keying in Large Numbers
Since the display cannot show more than 10 digits of a number, numbers greater
than 9,999,999,999 cannot be entered into the display by keying in all the digits
in the number. However, such numbers can be easily entered into the display if
the number is expressed in a mathematical shorthand called “scientific notation.”
To convert a number into scientific notation, move the decimal point until there
is only one digit (a nonzero digit) to its left. The resulting number is called the
“mantissa” of the original number, and the number of decimal places you moved
the decimal point is called the “exponent” of the original number. If you moved
the decimal point to the left, the exponent is positive; if you moved the decimal
point to the right (this would occur for numbers less than one), the exponent is
negative. To key the number into the display, simply key in the mantissa, press
Æ (enter exponent), then key in the exponent. If the exponent is negative,
press Þ after pressing Æ.
For example, to key in $1,781,400,000,000, we move the decimal point 12
places to the left, giving a mantissa of 1.7814 and an exponent of 12:
Numbers entered in scientific notation can be used in calculations just like any
other number.
The CLEAR Keys
Clearing a register or the display replaces the number in it with zero. Clearing
program memory replaces the instructions there with gi000. There are
several clearing operations on the HP 12C Platinum, as shown in the table
below:
Keystrokes Display
1.7814Æ12
1.7814 12
1,781,400,000,000 entered in
scientific notation.
Key(s) Clears:
O Display and X-register.
fCLEAR² Statistics registers (R
1
through R
6
), stack
registers, and display.
fCLEARÎ Program memory (only when pressed in
Program mode).
fCLEARG Financial registers.
fCLEARH Data storage registers, financial registers,
stack and LAST X registers, and display.
Section 1: Getting Started 19
The RPN and ALG Keys
The calculator can be set to perform arithmetic operations in either RPN
(Reverse Polish Notation) or ALG (Algebraic) mode.
In reverse polish notation (RPN) mode, the intermediate results of calculations
are stored automatically, hence you do not have to use parentheses.
In algebraic (ALG) mode, you perform addition, subtraction, multiplication, and
division in the traditional way.
To select RPN mode: Press f] to set the calculator to RPN mode. When the
calculator is in RPN mode, the RPN status indicator is lit.
To select ALG mode: Press f[ to set the calculator to ALG mode. When
the calculator is in ALG mode, the ALG status indicator is lit.
Example
Suppose you want to calculate 1 + 2 = 3.
In RPN mode, you enter the first number, press the \ key, enter the second
number, and finally press the arithmetic operator key: +.
In ALG mode, you enter the first number, press +, enter the second number,
and finally press the equals key: }.
In RPN mode and algebraic mode, the results of all calculations are listed.
However, in RPN mode only the results are listed, not the calculations.
Most examples in this manual (except those in Appendix B) assume that RPN
mode is selected. Some examples will also be correct if you are in ALG mode.
Simple Arithmetic Calculations in RPN Mode
In RPN mode, any simple arithmetic calculation involves two numbers and an
operation – addition, subtraction, multiplication, or division. To do such a
calculation on your HP 12C Platinum, you first tell the calculator the two
numbers, then tell the calculator the operation to be performed. The answer is
calculated when the operation key (+,-,§, or z) is pressed.
The two numbers should be keyed into the calculator in the order they would
appear if the calculation were written down on paper left-to-right. After keying
in the first number, press the \ key to tell the calculator that you have
completed entering the number. Pressing \ separates the second number to
be entered from the first number already entered.
RPN mode ALG mode
1 \ 2 + 1 + 2 }
20 Section 1: Getting Started
In summary, to perform an arithmetic operation:
1. Key in the first number.
2. Press \ to separate the second number from the first.
3. Key in the second number.
4. Press +,-,§, or z to perform the desired operation.
For example to calculate 13 ÷ 2, proceed as follows:
Notice that after you pressed \, two zeroes appeared following the decimal
point. This is nothing magical: the calculators display is currently set to show
two decimal places of every number that has been entered or calculated. Before
you pressed \, the calculator had no way of knowing that you had completed
entering the number, and so displayed only the digits you had keyed in. Pressing
\ tells the calculator that you have completed entering the number: it
terminates digit entry. You need not press \ after keying in the second
number because the +,-,§, and z keys also terminate digit entry. (In fact,
all keys terminate digit entry except for digit entry keys – digit keys, ., Þ,
and Æ – and prefix keys – f, g, ?, :, and (.)
Chain Calculations in RPN Mode
Whenever the answer has just been calculated and is therefore in the display, you
can perform another operator with this number by simply keying in the second
number and then pressing the operation key: you need not press \ to separate
the second number from the first. This is because when a number is keyed in
after a function key (such as +,-,§,z, etc.) is pressed, the result of that
prior calculation is stored inside the calculator – just as when the \ key is
pressed. The only time you must press the \ key to separate two numbers is
when you are keying them both in, one immediately following the other.
The HP 12C Platinum is designed so that each time you press a function key in
RPN mode, the calculator performs the operation then – not later – so that you
see the results of all intermediate calculations, as well as the “bottom line.”
Keystrokes (RPN mode) Display
13
13.
Keys the first number into the
calculator.
\
13.00
Pressing \ separates the second
number from the first.
2
2.
Keys the second number into the
calculator.
z
6.50
Pressing the operation key
calculates the answer.
Section 1: Getting Started 21
Example: Suppose you’ve written three checks without updating your
checkbook, and you’ve just deposited your paycheck for $1,053.00 into your
checking account. If your latest balance was $58.33 and the checks were written
for $22.95, $13.70, and $10.14, what is the new balance?
Solution: When written down on paper, this problem would read
58.33 – 22.95 – 13.70 – 10.14 + 1053
Keystrokes (RPN mode) Display
58.33
58.33
Keys the first number.
\
58.33
Pressing \ separates the second
number from the first.
22.95
22.95
Keys in the second number.
-
35.38
Pressing - subtracts the second
number from the first. The
calculator displays the result of this
calculation, which is the balance
after subtracting the first check.
13.70
13.70
Keys in the next number. Since a
calculation has just been
performed, do not press \; the
next number entered (13.70) is
automatically separated from the
one previously in the display
(35.38).
-
21.68
Pressing - subtracts the number
just entered from the number
previously in the display. The
calculator displays the result of this
calculation, which is the balance
after subtracting the second check.
10.14-
11.54
Keys in the next number and
subtracts it from the previous
balance. The new balance appears
in the display. (It’s getting rather
low!)
1053+
1,064.54
Keys in the next number – the
paycheck deposited – and adds it to
the previous balance. The new,
current balance appears in the
display.
22 Section 1: Getting Started
The preceding example demonstrates how the HP 12C Platinum calculates just
as you would using pencil and paper (except a lot faster!):
Let’s see this happening in a different type of calculation – one that involves
multiplying groups of two numbers and then adding the results. (This is the type
of calculation that would be required to total up an invoice consisting of several
items with different quantities and different prices.)
For example, consider the calculation of (3 × 4) + (5 × 6). If you were doing this
on paper, you would first do the multiplication in the first parentheses, then the
multiplication in the second parentheses, and finally add the results of the two
multiplications:
Your HP 12C Platinum calculates the answer in just the same way:
Notice that before doing step 2, you did not need to store or write down the result
of step 1: it was stored inside the calculator automatically. And after you keyed
in the 5 and the 6 in step 2, the calculator was holding two numbers (12 and 5)
inside for you, in addition to the 6 in the display. (The HP 12C Platinum can hold
a total of three numbers inside, in addition to the number in the display.) After
step 2, the calculator was still holding the 12 inside for you, in addition to the 30
in the display. You can see that the calculator holds the number for you, just as
you would have them written on paper, and then calculates with them at the
Keystrokes (RPN mode) Display
3\4§
12.00
Step 1: Multiply the numbers in the
first parentheses.
5\6§
30.00
Step 2: Multiply the numbers in the
second parentheses.
+
42.00
Step 3: Add the results of the two
multiplications.
Section 1: Getting Started 23
proper time, just as you would yourself.
2
But with the HP 12C Platinum, you
don’t need to write down the results of an intermediate calculation, and you don’t
even need to manually store it and recall it later.
By the way, notice that in step 2 you needed to press \ again. This is simply
because you were again keying in two numbers immediately following each
other, without performing a calculation in between.
To check your understanding of how to calculate with your HP 12C Platinum, try
the following problems yourself. Although these problems are relatively simple,
more complicated problems can be solved using the same basic steps. If you
have difficulty obtaining the answers shown, review the last few pages.
Storage Registers
Numbers (data) in the HP 12C Platinum are stored in memories called “storage
registers” or simply “registers.” (The singular term “memory” is sometimes used
in this handbook to refer to the entire collection of storage registers.) Four
special registers are used for storing numbers during calculations (these “stack
registers” are described in Appendix A), and another (called the LAST X
register) is used for storing the number last in the display before an operation is
performed. In addition to these registers into which numbers are stored
automatically, up to 20 “data storage” registers are available for manual storage
of numbers. These data storage registers are designated R
0
through R
9
and R
.0
through R
.9
. Fewer registers are available for data storage if a program has been
stored in the calculator (since the program is stored in some of those 20
registers), but a minimum of 7 registers is always available. Still other storage
registers – referred to as the “financial registers” – are reserved for numbers used
in financial calculations.
2.
Although you don’t need to know just how these numbers are stored and brought back at just
the right time, if you’re interested you can read all about it in Appendix A. By gaining a more
complete understanding of the calculators operation, you’ll use it more efficiently and
confidently, yielding a better return on the investment in your HP 12C Platinum.
34+()56+()× 77.00=
27 14()
14 38+()
-----------------------0.25=
5
31621++
--------------------------- 0 . 1 3=
24 Section 1: Getting Started
Storing and Recalling Numbers
To store the number from the display into a data storage register:
1. Press ? (store).
2. Key in the register number: 0 through 9 for registers R
0
through R
9
, or .0
through .9 for registers R
.0
through R
.9
.
Similarly, to recall a number from a storage register into the display, press :
(recall), then key in the register number. This copies the number from the storage
register into the display; the number remains unaltered in the storage register.
Furthermore, when this is done, the number previously in the display is
automatically held inside the calculator for a subsequent calculation, just as the
number in the display is held when you key in another number.
Example: Before you leave to call on a customer interested in your personal
computer, you store the cost of the computer ($3,250) and also the cost of a
printer ($2,500) in data storage registers. Later, the customer decides to buy six
computers and one printer. You recall the cost of the computer, multiply by the
quantity ordered, and then recall and add the cost of the printer to get the total
invoice.
Later that same day …
Keystrokes (RPN mode) Display
3250?1
3,250.00
Stores the cost of the computer in
R
1
.
2500?2
2,500.00
Stores the cost of the printer in R
2
.
; Turns the calculator off.
Keystrokes (RPN mode) Display
;
2,500.00
Turns the calculator back on.
:1
3,250.00
Recalls the cost of the computer to
the display.
6§
19,500.00
Multiplies the quantity ordered to
get the cost of the computers.
:2
2,500.00
Recalls the cost of the printer to the
display.
+
22,000.00
Total invoice.
Section 1: Getting Started 25
Clearing Storage Registers
To clear a single storage register – that is, to replace the number in it with zero –
merely store zero into it. You need not clear a storage register before storing data
into it; the storing operation automatically clears the register before the data is
stored.
To clear all storage registers at once – including the financial registers, the stack
registers, and the LAST X register – press fCLEARH.
3
This also clears the
display.
All storage registers are also cleared when Continuous Memory is reset (as
described on page 70).
Storage Register Arithmetic
Suppose you wanted to perform an arithmetic operation with the number in the
display and the number in a storage register, then store the result back into the
same register without altering the number in the display. The HP 12C Platinum
enables you to do all this in a single operation.
1. Press ?.
2. Press +,-,§, or z to specify the desired operation.
3. Key in the register number.
When storage register arithmetic is performed, the new number in the register is
determined according to the following rule:
Storage register arithmetic is possible with only registers R
0
through R
4
.
Example: In the example on page 21, we updated the balance in your
checkbook. Let’s suppose that because data is stored indefinitely in your
calculators Continuous Memory, you keep track of your checking account
balance in the calculator. You could use storage register arithmetic to quickly
update the balance after depositing or writing checks.
3.
CLEARH is not programmable.
26 Section 1: Getting Started
Keystrokes Display
58.33?0
58.33
Stores the current balance in
register R
0
.
22.95?-0
22.95
Subtracts the first check from the
balance in R
0
. Note that the display
continues to show the amount
subtracted; the answer is placed
only in R
0
.
13.70?-0
13.70
Subtracts the second check.
10.14?-0
10.14
Subtracts the third check.
1053?+0
1,053.00
Adds the deposit.
:0
1,064.54
Recalls the number in R
0
to check
the new balance.
27
Section 2
Percentage and Calendar
Functions
Percentage Functions
The HP 12C Platinum includes three keys for solving percentage problems: b,
à, and Z. You don’t need to convert percentages to their decimal
equivalents; this is done automatically when you press any of these keys. Thus,
4% need not be changed to 0.04; you key it in the way you see and say it: 4b.
Percentages
In RPN mode, to find the amount corresponding to a percentage of a number:
1. Key in the base number.
2. Press \.
3. Key in the percentage.
4. Press b.
For example, to find 14% of $300:
If the base number is already in the display as a result of a previous calculation,
you should not press \ before keying in the percentage – just as in a chain
arithmetic calculation.
Net amount
A net amount – that is, the base amount plus or minus the percentage amount –
can be calculated easily with your HP 12C Platinum, since the calculator holds
Keystrokes (RPN mode) Display
300
300.
Keys in the base number.
\
300.00
Pressing \ separates the next
number entered from the first
number, just as when an ordinary
arithmetic calculation is performed.
14
14.
Keys in the percentage.
b
42.00
Calculates the amount.
28 Section 2: Percentage and Calendar Functions
the base amount inside after you calculate a percentage amount. To calculate a
net amount, simply calculate the percentage amount, then press = or -.
Example: You’re buying a new car that lists for $13,250. The dealer offers you a
discount of 8%, and the sales tax is 6%. Find the amount the dealer is charging
you, then find the total cost to you, including tax.
Percent Difference
In RPN mode, to find the percent difference between two numbers:
1. Key in the base number.
2. Press \ to separate the other number from the base number.
3. Key in the other number.
4. Press à.
If the other number is greater than the base number, the percent difference will
be positive. If the other number is less than the base number, the percent
difference will be negative. Therefore, a positive answer indicates an increase,
while a negative answer indicates a decrease.
If you are calculating a percent difference over time, the base number is typically
the amount occurring first.
Example: Yesterday your stock fell from 58½ to 53¼ per share. What is the
percent change?
The à key can be used for calculations of the percent difference between a
wholesale cost and a retail cost. If the base number entered is the wholesale cost,
Keystrokes (RPN mode) Display
13250\
13,250.00
Keys in the base amount and
separates it from the percentage.
8b
1,060.00
Amount of discount.
-
12,190.00
Base amount less discount.
6b
731.40
Amount of tax (on $12,190).
=
12,921.40
Total cost: base amount less
discount plus tax.
Keystrokes Display
58.5\
58.50
Keys in the base number and
separates it from the other number.
53.25
53.25
Keys in the other number.
à
–8.97
Nearly a 9% decrease.
Section 2: Percentage and Calendar Functions 29
the percent difference is called the markup; if the base number entered is the
retail cost, the percent difference is called the margin. Examples of markup and
margin calculations are included in the HP 12C Platinum Solutions Handbook.
Percent of Total
In RPN mode, to calculate what percentage one number is of another:
1. Calculate the total amount by adding the individual amounts, just as in a
chain arithmetic calculation.
2. Key in the number whose percentage equivalent you wish to find.
3. Press Z.
Example: Last month, your company posted sales of $3.92 million in the U.S.,
$2.36 million in Europe, and $1.67 million in the rest of the world. What
percentage of the total sales occurred in Europe?
The HP 12C Platinum holds the total amount inside after a percent of total is
calculated. Therefore, to calculate what percentage another amount is of the
total:
1. Clear the display by pressing O.
2. Key in that amount.
3. Press Z again.
For example, to calculate what percent of the total sales in the preceding
example occurred in the U.S. and what percent occurred in the rest of the world:
Keystrokes (RPN mode) Display
3.92\
3.92
Keys in the first number and
separates it from the second.
2.36+
6.28
Adds the second number.
1.67+
7.95
Adds the third number to get the
total.
2.36
2.36
Keys in 2.36 to find what
percentage it is of the number in the
display.
Z
29.69
Europe had nearly 30% of the total
sales.
Keystrokes (RPN mode) Display
O3.92Z
49.31
The U.S. had about 49% of the total
sales.
O1.67 Z
21.01
The rest of the world had about
21% of the total sales.
30 Section 2: Percentage and Calendar Functions
To find what percentage a number is of a total, when you already know the total
number
1. Key in the total number.
2. Press \ to separate the other number from the total number.
3. Key in the number whose percentage equivalent you wish to find.
4. Press Z.
For example, if you already knew in the preceding example that the total sales
were $7.95 million and you wanted to find what percentage of that total occurred
in Europe:
Calendar Functions
The calendar functions provided by the HP 12C Platinum – D and Ò – can
handle dates from October 15, 1582 through November 25, 4046.
Date Format
For each of the calendar functions – and also for bond calculations (E and
S) – the calculator uses one of two date formats. The date format is used to
interpret dates when they are keyed into the calculator as well as for displaying
dates.
Month-Day-Year. To set the date format to month-day-year, press . To
key in a date with this format in effect:
1. Key in the one or two digits of the month.
2. Press the decimal point key (.).
3. Key in the two digits of the day.
4. Key in the four digits of the year.
Dates are displayed in the same format.
Keystrokes Display
7.95\
7.95
Keys in the total amount and
separates it from the next number.
2.36
2.36
Keys in 2.36 to find what
percentage it is of the number in the
display.
Z
29.69
Europe had nearly 30% of the total
sales.
Section 2: Percentage and Calendar Functions 31
For example, to key in April 7, 2003:
Day-Month-Year. To set the date format to day-month-year, press . To
key in a date with this format in effect:
1. Key in the one or two digits of the day.
2. Press the decimal point key (.).
3. Key in the two digits of the month.
4. Key in the four digits of the year.
For example, to key in 7 April, 2003:
When the date format is set to day-month-year, the D.MY status indicator in the
display is lit. If D.MY is not lit, the date format is set to month-day-year.
The date format remains set to what you last specified until you change it; it is
not reset each time the calculator is turned on. However, if Continuous Memory
is reset, the date format is set to month-day-year.
Future or Past Dates
To determine the date and day that is a given number of days from a given date:
1. Key in the given date and press \.
2. Key in the number of days.
3. If the other date is in the past, press Þ.
4. Press gD.
The answer calculated by the D function is displayed in a special format. The
numbers of the month, day, and year (or day, month, and year) are separated by
digit separators, and the digit at the right of the displayed answer indicates the
day of the week: 1 for Monday through 7 for Sunday.
4
Keystrokes Display
4.072003
4.072003
Keystrokes Display
7.042003
7.042003
4.
The day of the week indicated by the D function may differ from that recorded in history
for dates when the Julian calendar was in use. The Julian calendar was standard in England
and its colonies until September 14, 1752, when they switched to the Gregorian calendar.
Other countries adopted the Gregorian calendar at various times.
32 Section 2: Percentage and Calendar Functions
Example: If you purchased a 120-day option on a piece of land on 14 May 2003,
what would be the expiration date? Assume that you normally express dates in
the day-month-year format.
When D is executed as an instruction in a running program, the calculator
pauses for about 1 second to display the result, then resumes program execution.
Number of Days Between Dates
To calculate the number of days between two given dates:
1. Key in the earlier date and press \.
2. Key in the later date and press .
The answer shown in the display is the actual number of days between the two
dates, including leap days (the extra days occurring in leap years), if any. In
addition, the HP 12C Platinum also calculates the number of days between the
two dates on the basis of a 30-day month. This answer is held inside the
calculator; to display it, press ~. Pressing ~ again will return the original
answer to the display.
Example: Simple interest calculations can be done using either the actual
number of days or the number of days counted on the basis of a 30-day month.
What would be the number of days counted each way, to be used in calculating
the simple interest accruing from June 3, 2003 to October 14, 2004? Assume that
you normally express dates in the month-day-year format.
Keystrokes Display
7.04
Sets date format to day-month-
year. (Display shown assumes
date remains from preceding
example. The full date is not
now displayed because the
display format is set to show
only two decimal places, as
described in Section 5.)
14.052003\
14.05
Keys in date and separates it
from number of days to be
entered.
120gD
11,09,2003 4
The expiration date is 11
September 2003, a Thursday.
Section 2: Percentage and Calendar Functions 33
Keystrokes Display
11.09
Sets date format to month-day-year.
(Display shown assumes date
remains from preceding example.)
6.032003\
6.03
Keys in earlier date and separates it
from the later date.
10.152004
500.00
Keys in later date. Display shows
actual number of days.
~
492.00
Number of days counted on the
basis of a 30-day month.
34
Section 3
Basic Financial Functions
The Financial Registers
In addition to the data storage registers discussed on page 23, the HP 12C
Platinum has five special registers in which numbers are stored for financial
calculations. These registers are designated n, i, PV, PMT, and FV. The first five
keys on the top row of the calculator are used to store a number from the display
into the corresponding register, to calculate the corresponding financial value
and store the result into the corresponding register, or to display the number
stored in the corresponding register.
5
Storing Numbers Into the Financial Registers
To store a number into a financial register, key the number into the display, then
press the corresponding key (n, ¼, $, P, or M).
Displaying Numbers in the Financial Registers
To display a number stored in a financial register, press : followed by the
corresponding key.
6
Clearing the Financial Registers
Every financial function uses numbers stored in several of the financial registers.
Before beginning a new financial calculation, it is good practice to clear all of
the financial registers by pressing fCLEARG. Frequently, however, you
may want to repeat a calculation after changing a number in only one of the
financial registers. To do so, do not press fCLEARG; instead, simply store
the new number in the register. The numbers in the other financial registers
remain unchanged.
5.
Which operation is performed when one of these keys is pressed depends upon the last
preceding operation performed: If a number was just stored into a financial register (using
n, ¼, $, P, M, A, or C), pressing one of these five keys calculates the
corresponding value and stores it into the corresponding register; otherwise pressing one of
these five keys merely stores the number from the display into the corresponding register.
6.
It’s good practice to press the corresponding key twice after :, since often you may want
to calculate a financial value right after displaying another financial value. As indicated in the
preceding footnote, if you wanted to display FV and then calculate PV, for example, you
should press :MM$. If you didn’t press M the second time, pressing
$ would
store FV in the PV register rather than calculating PV, and to calculate PV you would have to
press $ again.
Section 3: Basic Financial Functions 35
The financial registers are also cleared when you press fCLEARH and
when Continuous Memory is reset (as described on page 70).
Simple Interest Calculations
The HP 12C Platinum simultaneously calculates simple interest on both a 360-
day basis and a 365-day basis. You can display either one, as described below.
Furthermore, with the accrued interest in the display, you can calculate the total
amount (principal plus accrued interest) by pressing +.
1. Key in or calculate the number of days, then press n.
2. Key in the annual interest rate, then press ¼.
3. Key in the principal amount, then press Þ$.
7
4. Press to calculate and display the interest accrued on a 360-day
basis.
5. If you want to display the interest accrued on a 365-day basis, press
d~.
6. Press + to calculate the total of the principal and the accrued interest now
in the display.
The quantities n, i, and PV can be entered in any order.
Example 1: Your good friend needs a loan to start his latest enterprise and has
requested that you lend him $450 for 60 days. You lend him the money at 7%
simple interest, to be calculated on a 360-day basis. What is the amount of
accrued interest he will owe you in 60 days, and what is the total amount owed?
Example 2: Your friend agrees to the 7% interest on the loan from the preceding
example, but asks that you compute it on a 365-day basis rather than a 360-day
7.
Pressing the $ key stores the principal amount in the PV register, which then contains the
present value of the amount on which interest will accrue. The Þ key is pressed first to
change the sign of the principal amount before storing it in the PV register. This is required
by the cash flow sign convention, which is applicable primarily to compound interest
calculations.
Keystrokes (RPN mode) Display
60n
60.00
Stores the number of days.
7¼
7.00
Stores the annual interest rate.
450Þ$
–450.00
Stores the principal.
5.25
Accrued interest, 360-day basis.
+
455.25
Total amount: principal plus
accrued interest.
36 Section 3: Basic Financial Functions
basis. What is the amount of accrued interest he will owe you in 60 days, and
what is the total amount owed?
Financial Calculations and the Cash Flow
Diagram
The concepts and examples presented in this section are representative of a wide
range of financial calculations. If your specific problem does not appear to be
illustrated in the pages that follow, don’t assume that the calculator is not capable
of solving it. Every financial calculation involves certain basic elements; but the
terminology used to refer to these elements typically differs among the various
segments of the business and financial communities. All you need to do is
identify the basic elements in your problem, and then structure the problem so
that it will be readily apparent what quantities you need to tell the calculator and
what quantity you want to solve for.
An invaluable aid for using your calculator in a financial calculation is the cash
flow diagram. This is simply a pictorial representation of the timing and
direction of financial transactions, labeled in terms that correspond to keys on
the calculator.
The diagram begins with a horizontal line, called a time line. It represents the
duration of a financial problem, and is divided into compounding periods. For
example, a financial problem that transpires over 6 months with monthly
compounding would be diagrammed like this:
The exchange of money in a problem is depicted by vertical arrows. Money you
receive is represented by an arrow pointing up from the point in time line when
the transaction occurs; money you pay out is represented by an arrow pointing
down.
Keystrokes (RPN mode) Display
60n
7¼
450Þ$
60.00
7.00
–450.00
If you have not altered the
numbers in the n, i, and PV
registers since the preceding
example, you may skip these
keystrokes.
fÏd~
5.18
Accrued interest, 365-day
basis.
+
455.18
Total amount: principal plus
accrued interest.
Section 3: Basic Financial Functions 37
Suppose you deposited (paid out) $1,000 into an account that pays 6% annual
interest and is compounded monthly, and you subsequently deposited an
additional $50 at the end of each month for the next 2 years. The cash flow
diagram describing the problem would look like this:
The arrow pointing up at the right of the diagram indicates that money is
received at the end of the transaction. Every completed cash flow diagram must
include at least one cash flow in each direction. Note that cash flows
corresponding to the accrual of interest are not represented by arrows in the cash
flow diagram.
The quantities in the problem that correspond to the first five keys on the top row
of the keyboard are now readily apparent from the cash flow diagram.
z n is the number of compounding periods. This quantity can be expressed in
years, months, days, or any other time unit, as long as the interest rate is
expressed in terms of the same basic compounding period. In the problem
illustrated in the cash flow diagram above, n = 2 × 12.
The form in which n is entered determines whether or not the calculator
performs financial calculations in Odd-Period mode (as described on pages
51 through 54). If n is a noninteger (that is, there is at least one nonzero
digit to the right of the decimal point), calculations of i, PV, PMT, and FV
are performed in Odd-Period mode.
38 Section 3: Basic Financial Functions
z i is the interest rate per compounding period. The interest rate shown in the
cash flow diagram and entered into the calculator is determined by
dividing the annual interest rate by the number of compounding periods. In
the problem illustrated above, i = 6% ÷ 12.
z PV – the present value – is the initial cash flow or the present value of a
series of future cash flows. In the problem illustrated above, PV is the
$1,000 initial deposit.
z PMT is the period payment. In the problem illustrated above PMT is the
$50 deposited each month. When all payments are equal, they are referred
to as annuities. (Problems involving equal payments are described in this
section under Compound Interest Calculations; problems involving
unequal payments can be handled as described in Section 4 under
Discounted Cash Flow Analysis: NPV and IRR. Procedures for calculating
the balance in a savings account after a series of irregular and/or unequal
deposits are included in the HP 12C Platinum Solutions Handbook.)
z FV – the future value – is the final cash flow or the compounded value of a
series of prior cash flows. In the particular problem illustrated above, FV is
unknown (but can be calculated).
Solving the problem is now basically a matter of keying in the quantities
identified in the cash flow diagram using the corresponding keys, and then
calculating the unknown quantity by pressing the corresponding key. In the
particular problem illustrated in the cash flow diagram above, FV is the unknown
quantity; but in other problems, as we shall see later, n, i, PV, or PMT could be
the unknown quantity. Likewise, in the particular problem illustrated above there
are four known quantities that must be entered into the calculator before solving
for the unknown quantity; but in other problems only three quantities may be
known – which must always include n or i.
The Cash Flow Sign Convention
When entering the PV, PMT, and FV cash flows, the quantities must be keyed
into the calculator with the proper sign, + (plus) or – (minus), in accordance with
The Cash Flow Sign Convention: Money received (arrow pointing up) is
entered or displayed as a positive value (+). Money paid out (arrow
pointing down) is entered or displayed as a negative value (–).
The Payment Mode
One more bit of information must be specified before you can solve a problem
involving periodic payments. Such payments can be made either at the beginning
of a compounding period (payments in advance, or annuities due) or at the end of
the period (payments in arrears, or ordinary annuities). Calculations involving
Section 3: Basic Financial Functions 39
payments in advance yield different results than calculations involving payments
in arrears. Illustrated below are portions of cash flow diagrams showing
payments in advance (Begin) and payments in arrears (End). In the problem
illustrated in the cash flow diagram above, payments are made in arrears.
Regardless of whether payments are made in advance or in arrears, the number
of payments must be the same as the number of compounding periods.
To specify the payment mode:
z Press if payments are made at the beginning of the compounding
periods.
z Press if payments are made at the end of the compounding
periods.
The BEGIN status indicator is lit when the payment mode is set to Begin. If
BEGIN is not lit, the payment mode is set to End.
The payment mode remains set to what you last specified until you change it; it
is not reset each time the calculator is turned on. However, if Continuous
Memory is reset, the payment mode will be set to End.
Generalized Cash Flow Diagrams
Examples of various kinds of financial calculations, together with the applicable
cash flow diagrams, appear under Compound Interest Calculations later in this
section. If your particular problem does not match any of those shown, you can
solve it nevertheless by first drawing a cash flow diagram, then keying the
quantities identified in the diagram into the corresponding registers. Remember
always to observe the sign convention when keying in PV, PMT, and FV.
The terminology used for describing financial problems varies among the
different segments of the business and financial communities. Nevertheless,
most problems involving compound interest can be solved by drawing a cash
flow diagram in one of the following basic forms. Listed below each form are
some of the problems to which that diagram applies.
40 Section 3: Basic Financial Functions
Section 3: Basic Financial Functions 41
Compound Interest Calculations
Specifying the Number of Compounding Periods and the
Periodic Interest Rate
Interest rates are usually quoted at the annual rate (also called the nominal rate):
that is, the interest rate per year. However, in compound interest problems, the
interest rate entered into i must always be expressed in terms of the basic
compounding period, which may be years, months, days, or any other time unit.
For example, if a problem involves 6% annual interest compounded quarterly for
5 years, n – the number of quarters – would be 5 × 4 = 20 and i – the interest rate
per quarter – would be 6% ÷ 4 = 1.5%. If the interest were instead compounded
monthly, n would be 5× 12 = 60 and i would be 6% ÷ 12 = 0.5%.
If you use the calculator to multiply the number of years by the number of
compounding periods per year, pressing n then stores the result in n. The same
is true for i. Values of n and i are calculated and stored like this in Example 2 on
page 48.
If interest is compounded monthly, you can use a shortcut provided on the
calculator to calculate and store n and i:
z To calculate and store n, key the number of years into the display, then
press gA.
z To calculate and store i, key the annual rate into the display, then press
gC.
Note that these keys not only multiply or divide the displayed number by 12;
they also automatically store the result in the corresponding register, so you need
not press the n or ¼ key next. The A and C keys are used in Example 1
on page 48.
Calculating the Number of Payments or Compounding
Periods
1. Press fCLEARG to clear the financial registers.
2. Enter the periodic interest rate, using ¼ or C.
3. Enter at least two of the following values:
4. If a PMT was entered, press or to set the payment mode.
5. Press n to calculate the number of payments or periods.
z Present value, using $.
z Payment amount, using P.
z Future value, using M.
Note: Remember to
observe the cash flow
sign convention.
42 Section 3: Basic Financial Functions
If the answer calculated is not an integer (that is, there would be nonzero digits to
the right of the decimal point), the calculator rounds the answer up to the next
higher integer before storing it in the n register and displaying it.
8
For example,
if n were calculated as 318.15, 319.00 would be the displayed answer.
n is rounded up by the calculator to show the total number of payments needed:
n–1 equal, full payments, and one final, smaller payment. The calculator does
not automatically adjust the values in the other financial registers to reflect
n equal payments; rather, it allows you to choose which, if any, of the values to
adjust.
9
Therefore, if you want to know the value of the final payment (with
which you can calculate a balloon payment) or desire to know the payment value
for n equal payments, you will need to press one of the other financial keys, as
shown in the following two examples.
Example 1: You’re planning to build a log cabin on your vacation property. Your
rich uncle offers you a $35,000 loan at 10.5% interest. If you make $325
payments at the end of each month, how many payments will be required to pay
off the loan, and how many years will this take?
8.
The calculator will round n down to the next lower integer if the fractional portion of n is less
than 0.005.
9.
After calculating n, pressing ¼,$,P, or M will recalculate the value in the
corresponding financial register.
Keystrokes Display
fCLEARG
10.5gC
0.88
Calculates and stores i.
35000$
35,000.00
Stores PV.
325ÞP
–325.00
Stores PMT (with minus sign for
cash paid out).
–325.00
Sets the payment mode to End.
n
328.00
Number of payments required.
12z
27.33
Twenty-seven years and four
months.
Section 3: Basic Financial Functions 43
Because the calculator rounds the calculated value of n up to the next higher
integer, in the preceding example it is likely that – while 328 payments will be
required to pay off the loan – only 327 full payments of $325 will be required,
the next and final payment being less than $325. You can calculate the final,
fractional, 328th payment as follows:
Alternatively, you could make the fractional payment together with the 327th
payment. (Doing so will result in a somewhat smaller total of all payments, since
you will not have to pay interest during the 328th payment period.) You can
calculate this final, larger, 327th payment (essentially a balloon payment) as
follows:
Instead of having a fractional (or balloon) payment at the end of the loan, you
might wish to make 327 or 328 equal payments. Refer to “Calculating the
Payment Amount” on page 48 for a complete description of this procedure.
Example 2: You’re opening a savings account today (the middle of the month)
with a $775 deposit. The account pays 6¼% interest compounded semimonthly.
If you make semimonthly deposits of $50 beginning next month, how long will it
take for your account to reach $4000?
Keystrokes (RPN mode) Display
328n
328.00
Stores total number of payments.
a
a You could skip this step, since 328 is already stored in the n register. If you do so, how-
ever, you will need to press M twice in the next step (for the reason discussed in the
first footnote on page 34; you would not have to press M twice if you had not pressed
12z after w in the example above.) We choose to show this and the following exam-
ple in a parallel format so that the procedure is easy to remember: the number you key
is the number of the final payment—either the fractional payment or the balloon pay-
ment—whose amount is to be calculated.
M
181.89
Calculates FV – which equals the
overpayment if 328 full payments
were made.
:P
–325.00
Recalls payment amount.
+
–143.11
Final, fractional payment.
Keystrokes (RPN mode) Display
327n
327.00
Stores number of full payments.
M
–141.87
Calculates FV – which is the
balance remaining after 327 full
payments.
:P
–325.00
Recalls payment amount.
+
–466.87
Final, balloon payment.
44 Section 3: Basic Financial Functions
As in Example 1, it is likely that only 57 full deposits will be required, the next
and final deposit being less than $50. You can calculate this final, fractional, 58th
deposit as in Example 1, except that for this example you must subtract the
original FV. (In Example 1, the original FV was zero.) The procedure is as
follows:
Keystrokes (RPN mode) Display
fCLEARG
6.25\24
0.26
Calculates and stores i.
775Þ$
–775.00
Stores PV (with minus sign for cash
paid out).
50ÞP
–50.00
Stores PMT (with minus sign for
cash paid out).
4000M
4,000.00
Stores FV.
4,000.00
Sets the payment mode to End.
n
58.00
Number of semimonthly deposits.
2z
29.00
Number of months.
Keystrokes (RPN mode) Display
MM
4,027.27
Calculates FV – which equals the
balance in the account if 58 full
deposits were made.
a
:P
–50.00
Recalls amount of deposits.
+
3,977.27
Calculates the balance in the
account if 57 full deposits were
made and interest accrued during
the 58
th
month.
b
4000-
–22.73
Calculates final, fractional, 58
th
deposit required to reach $4,000.
Section 3: Basic Financial Functions 45
Calculating the Periodic and Annual Interest Rates
1. Press fCLEARG to clear the financial registers.
2. Enter the number of payments or periods, using n or A.
3. Enter at least two of the following values:
4. If a PMT was entered, press or to set the payment mode.
5. Press ¼ to calculate the periodic interest rate.
6. To calculate the annual interest rate, key in the number of periods per year,
then press §.
Example: What annual interest rate must be obtained to accumulate $10,000 in
8 years on an investment of $6,000 with quarterly compounding?
a In this example, M must be pressed twice, since the preceding key pressed was z.
If we had stored the number of deposits in n (as we did following Example 1), we
would have to press M only once here, since the preceding key pressed would have
been w (as it was following Example 1). Remember that it is not necessary to store
the number of payments in n before calculating the amount of the final, fractional pay-
ment. (Refer to the preceding footnote.)
b You might think that we could calculate the balance in the account after 57 full deposits
were made simply by storing that number in n and then calculating FV, as we did using
the second method following Example 1. However, this balance would not include the
interest accrued during the 58
th
month.
z Present value, using $.
z Payment amount, using P.
z Future value, using M.
Note: Remember to
observe the cash flow
sign convention.
46 Section 3: Basic Financial Functions
Calculating the Present Value
1. Press fCLEARG to clear the financial registers.
2. Enter the number of payments or periods, using n or A.
3. Enter the periodic interest rate, using ¼ or C.
4. Enter either or both of the following:
5. If a PMT was entered, press or to set the payment mode.
6. Press $ to calculate the present value.
Example 1: You’re financing a new car purchase with a loan from an institution
that requires 15% interest compounded monthly over the 4-year term of the loan.
If you can make payments of $150 at the end of each month and your down
payment will be $1,500, what is the maximum price you can pay for the car?
(Assume the purchase date is one month prior to the date of the first payment.)
Keystrokes (RPN mode) Display
fCLEARG
8\4§n
32.00
Calculates and stores n.
6000Þ$
–6,000.00
Stores PV (with minus sign for cash
paid out).
10000M
10,000.00
Stores FV.
¼
1.61
Periodic (quarterly) interest rate.
4§
6.44
Annual interest rate.
z Payment amount, using P.
z Future value, using M.
Note: Remember to
observe the cash flow
sign convention.
Section 3: Basic Financial Functions 47
Example 2: A development company would like to purchase a group of
condominiums with an annual net cash flow of $17,500. The expected holding
period is 5 years, and the estimated selling price at that time is $540,000.
Calculate the maximum amount the company can pay for the condominiums in
order to realize at least a 12% annual yield.
Keystrokes Display
fCLEARG
4gA
48.00
Calculates and stores n.
15gC
1.25
Calculates and stores i.
150ÞP
–150.00
Stores PMT (with minus sign for
cash paid out).
–150.00
Sets payment mode to End.
$
5,389.72
Maximum amount of loan.
1500+
6,889.72
Maximum purchase price.
Keystrokes Display
fCLEARG
5n
5.00
Stores n.
12¼
12.00
Stores i.
17500P
17,500.00
Stores PMT. Unlike in the
previous problem, here PMT
is positive since it represents
cash received.
540000M
540,000.00
Stores FV.
540,000.00
Sets payment mode to End.
$
–369,494.09
The maximum purchase price
to provide a 12% annual
yield. PV is displayed with a
minus sign since it represents
cash paid out.
48 Section 3: Basic Financial Functions
Calculating the Payment Amount
1. Press fCLEARG to clear the financial registers.
2. Enter the number of payments or periods, using n or A.
3. Enter the periodic interest rate, using ¼ or C.
4. Enter either or both of the following:
5. Press or to set the payment mode.
6. Press P to calculate the payment amount.
Example 1: Calculate the payment amount on a 29-year, $43,400 mortgage at
14¼% annual interest.
Example 2: Looking forward to retirement, you wish to accumulate $60,000
after 15 years by making deposits in an account that pays 9¾% interest
compounded semiannually. You open the account with a deposit of $3,200 and
intend to make semiannual deposits, beginning six months later, from your
profit-sharing bonus paychecks. Calculate how much these deposits should be.
z Present value, using $.
z Future value, using M.
Note: Remember to
observe the cash flow
sign convention.
Keystrokes Display
fCLEARG
29gA
348.00
Calculates and stores n.
14.25gC
1.19
Calculates and stores i.
43400$
43,400.00
Stores PV.
43,400.00
Sets payment mode to End.
P
–523.99
Monthly payment (with minus sign
for cash paid out).
Section 3: Basic Financial Functions 49
Calculating the Future Value
1. Press fCLEARG to clear the financial registers.
2. Enter the number of payments or periods, using n or A.
3. Enter the periodic interest rate, using ¼ or C.
4. Enter either or both of the following:
5. If a PMT was entered, press or to set the payment mode.
6. Press M to calculate the future value.
Keystrokes Display
fCLEARG
15\2§n
30.00
Calculates and stores n.
9.75\2
4.88
Calculates and stores i.
3200Þ$
–3200.00
Stores PV (with minus sign for cash
paid out).
60000M
60,000.00
Stores FV.
60,000.00
Sets payment mode to End.
P
–717.44
Semiannual payment (with minus
sign for cash paid out).
z Present value, using $.
z Payment amount, using P.
Note: Remember to
observe the cash flow
sign convention.
50 Section 3: Basic Financial Functions
Example 1: In Example 1 on page 48, we calculated that the payment amount on
a 29-year, $43,400 mortgage at 14¼% annual interest is $523.99. If the seller
requests a balloon payment at the end of 5 years, what would be the amount of
the balloon?
Example 2: If you deposit $50 a month (at the beginning of each month) into a
new account that pays 6¼% annual interest compounded monthly, how much
will you have in the account after 2 years?
Keystrokes Display
fCLEARG
5gA
60.00
Calculates and stores n.
14.25gC
1.19
Calculates and stores i.
43400$
43,400.00
Stores PV.
523.99ÞP
–523.99
Stores PMT (with minus sign for
cash paid out).
–523.99
Sets payment mode to End.
M
–42,652.37
Amount of balloon payment.
Section 3: Basic Financial Functions 51
Example 3: Property values in an unattractive area are depreciating at the rate of
2% per year. Assuming this trend continues, calculate the value in 6 years of
property presently appraised at $32,000.
Odd-Period Calculations
The cash flow diagrams and examples presented so far have dealt with financial
transactions in which interest begins to accrue at the beginning of the first
regular payment period. However, interest often begins to accrue prior to the
beginning of the first regular payment period. The period from the date interest
begins accruing to the date of the first payment, being not equal to the regular
payment periods is sometimes referred to as an “odd first period”. For simplicity,
in using the HP 12C Platinum we will always regard the first period as equal to
the remaining periods, and we will refer to the period between the date interest
begins accruing and the beginning of the first payment period as simply the “odd
Keystrokes Display
fCLEARG
2gA
24.00
Calculates and stores n.
6.25gC
0.52
Calculates and stores i.
50ÞP
–50.00
Stores PMT (with minus sign for
cash paid out).
–50.00
Sets payment mode to Begin.
M
1,281.34
Balance after 2 years.
Keystrokes Display
fCLEARG
6n
6.00
Stores n.
2Þ¼
–2.00
Stores i (with minus sign for a
“negative interest rate”).
32000Þ$
–32,000.00
Stores PV (with minus sign for cash
paid out).
M
28,346.96
Property value after 6 years.
52 Section 3: Basic Financial Functions
period” or the “odd days”. (Note that the odd period is always assumed by the
calculator to occur before the first full payment period.) The following two cash
flow diagrams represent transactions including an odd period for payments in
advance (Begin) and for payments in arrears (End).
.
You can calculate i, PV, PMT, and FV for transactions involving an odd period
simply by entering a noninteger n. (A noninteger is a number with at least one
nonzero digit to the right of the decimal point.) This places the calculator in Odd-
Period mode.
10
The integer part of n (the part to the left of the decimal point)
specifies the number of full payment periods, and the fractional part (the part to
the right of the decimal) specifies the length of the odd period as a fraction of a
full period. The odd period, therefore, cannot be greater than one full period.
The fractional part of n can be determined using either the actual number of odd
days or the number of odd days counted on the basis of a 30-day month.
11
The
Ò function can be used to calculate the number of odd days either way. The
fractional part of n is a fraction of a payment period, so the number of odd days
10.
Calculations of i, PMT, and FV are performed using the present value at the end of the odd
period. This is equal to the number in the PV register plus the interest accrued during the odd
period. When calculating PV in Odd-Period mode, the calculator returns a value equal to the
present value at the beginning of the odd period and stores it in the PV register.
After calculating i, PV, PMT, or FV in Odd-Period mode, you should not try to calculate n. If
you do, the calculator will switch out of Odd-Period mode and compute n without taking the
odd period into account. The values in the other financial registers will correspond to the new
n, but the original assumptions for the problem will be changed.
11.
The two methods of counting odd days will yield slightly different answers. If you are
calculating i to determine the annual percentage rate (APR) for an odd-period transaction, the
lower APR will result if the calculation uses the greater number of odd days determined using
the two methods.
Section 3: Basic Financial Functions 53
must be divided by the number of days in a period. If interest is compounded
monthly, for this number you can use either 30, 365/12, or (if the odd period falls
entirely within a single month) the actual number of days in that month. Usually,
a monthly period is taken to be 30 days long.
At your option, the calculations of i, PV, PMT, and FV can be performed with
either simple interest or compound interest accruing during the odd period. If the
C status indicator in the display is not lit, simple interest is used. To specify
compound interest, turn the C indicator on by pressing .
12
Pressing
again turns the C indicator off, and calculations will then be performed
using simple interest for the odd period.
Example 1: A 36-month loan for $4,500 accrues interest at a 15% annual
percentage rate (APR), with the payments made at the end of each month. If
interest begins accruing on this loan on February 15, 2003 (so that the first
period begins on March 1, 2003), calculate the monthly payment, with the odd
days counted on the basis of a 30-day month and compound interest used for the
odd period.
12.
is not programmable.
Keystrokes (RPN mode) Display
fCLEARG Clears financial registers.
Sets date format to month-day-year.
Sets payment mode to End.
Turns on the C indicator in the
display, so that compound interest
will be used for the odd period.
2.152003\
2.15
Keys in the date interest begins
accruing and separates it from the
next date entered.
3.012003
3.012003
Keys in the date of the beginning of
the first period.
14.00
Actual number of odd days.
~
16.00
Number of odd days counted on the
basis of a 30-day month.
30z
0.53
Divides by the length of a monthly
period to get the fractional part of n.
36+n
36.53
Adds the fractional part of n to the
number of complete payment
periods, then stores the result in n.
15gC
1.25
Calculates and stores i.
4500$
4,500.00
Stores PV.
P
–157.03
Monthly payment.
54 Section 3: Basic Financial Functions
Example 2: A 42-month car loan for $3,950 began accruing interest on July 19,
2003, so that the first period began on August 1, 2003. Payments of $120 are
made at the end of each month. Calculate the annual percentage rate (APR),
using the actual number of odd days and simple interest for the odd period.
Amortization
The HP 12C Platinum enables you to calculate the amounts applied toward
principal and toward interest from a single loan payment or from several
payments, and also tells you the remaining balance of the loan after the payments
are made.
13
Keystrokes (RPN mode) Display
fCLEARG Clears financial registers.
Turns off the C indicator in the
display, so that simple interest will
be used for the odd period.
7.192003\
7.19
Keys in the date interest begins
accruing and separates it from the
next date entered.
8.012003
8.012003
Keys in the date of the beginning of
the first period.
13.00
Actual number of odd days.
30z
0.43
Divides by the length of a monthly
period to get the fractional part of n.
42+n
42.43
Adds the fractional part of n to the
number of complete payment
periods, then stores the result in n.
3950$
3,950.00
Stores PV.
120ÞP
–120.00
Stores PMT (with minus sign for
cash paid out).
¼
1.16
Periodic (monthly) interest rate.
12§
13.95
Annual percentage rate (APR).
13.
All amounts calculated when f! is pressed are automatically rounded to the number of
decimal places specified by the display format. (The display format is described in Section
5.) This rounding affects the number inside the calculator as well as how the number appears
in the display. The amounts calculated on your HP 12C Platinum may differ from those on
the statements of lending institutions by a few cents, since different rounding techniques are
sometimes used. To calculate answers rounded to a different number of decimal places, press
f followed by the number of decimal places desired before you press f!.
Section 3: Basic Financial Functions 55
To obtain an amortization schedule:
1. Press fCLEARG to clear the financial registers.
2. Enter the periodic interest rate, using ¼ or C.
3. Enter the amount of the loan (the principal), using $.
4. Key in the periodic payment, then press ÞP (the sign of PMT must
be negative, in accordance with the cash flow sign convention).
5. Press or (for most direct reduction loans) to set the
payment mode.
6. Key in the number of payments to be amortized.
7. Press f! to display the amount from those payments applied toward
interest.
8. Press ~ to display the amount from those payments applied toward the
principal.
9. To display the number of payments just amortized, press dd.
10. To display the remaining balance of the loan, press :$.
11. To display the total number of payments amortized, press :n.
Example: For a house you’re about to buy, you can obtain a 25-year mortgage
for $50,000 at 13¼% annual interest. This requires payments of $573.35 (at the
end of each month). Find the amounts that would be applied to interest and to the
principal from the first years payments.
Keystrokes Display
fCLEARG
13.25gC
1.10
Enters i.
50000$
50,000.00
Enters PV.
573.35ÞP
–573.35
Enters PMT (with minus sign for
cash paid out).
–573.35
Sets payment mode to End.
12f!
–6,608.89
Portion of first years payments (12
months) applied to interest.
~
–271.31
Portion of first years payments
applied to principal.
:$
49,728.69
Balance remaining after 1 year.
:n
12.00
Total number of payments
amortized.
56 Section 3: Basic Financial Functions
The number of payments keyed in just before f! is pressed is taken to be
the payments following any that have already been amortized. Thus, if you now
press 12f!, your HP 12C Platinum will calculate the amounts applied to
interest and to the principal from the second years payments (that is, the second
12 months):
Pressing :$ or :n displays the number in the PV or n register. When
you did so after each of the last two calculations, you may have noticed that PV
and n had been changed from their original values. The calculator does this so
that you can easily check the remaining balance and the total number of
payments amortized. But because of this, if you want to generate a new
amortization schedule from the beginning, you must reset PV to its original value
and reset n to 0.
For example, suppose you now wanted to generate an amortization schedule for
each of the first two months:
Keystrokes Display
12f!
–6,570.72
Portion of second years payments
applied to interest.
~
–309.48
Portion of second years payments
applied to principal.
dd
12.00
Number of payments just
amortized.
:$
49,419.21
Balance remaining after 2 years.
:n
24.00
Total number of payments
amortized.
Keystrokes Display
50000$
50,000.00
Resets PV to original value.
0n
0.00
Resets n to zero.
1f!
–552.08
Portion of first payment applied to
interest.
~
–21.27
Portion of first payment applied to
principal.
1f!
–551.85
Portion of second payment applied
to interest.
~
–21.50
Portion of second payment applied
to principal.
:n
2.00
Total number of payments
amortized.
Section 3: Basic Financial Functions 57
If you want to generate an amortization schedule but do not already know the
monthly payment:
1. Calculate PMT as described on page 48.
2. Press 0n to reset n to zero.
3. Proceed with the amortization procedure listed on page 55 beginning with
step 6.
Example: Suppose you obtained a 30-year mortgage instead of a 25-year
mortgage for the same principal ($50,000) and at the same interest rate (13¼%)
as in the preceding example. Calculate the monthly payment, then calculate the
amounts applied to interest and to the principal from the first month’s payment.
Since the interest rate is not being changed, do not press fCLEARG; to
calculate PMT, just enter the new value for n, reset PV, then press P.
Keystrokes Display
30gA
360.00
Enters n.
50000$
50,000.00
Enters PV.
P
–562.89
Monthly payment.
0n
0.00
Resets n to zero.
1f!
–552.08
Portion of first payment applied to
interest.
~
–10.81
Portion of first payment applied to
principal.
:$
49,989.19
Remaining balance.
58
Section 4
Additional Financial Functions
Discounted Cash Flow Analysis: NPV and IRR
The HP 12C Platinum provides functions for the two most widely-used methods
of discounted cash flow analysis: l (net present value) and L (internal rate
of return). These functions enable you to analyze financial problems involving
cash flows (money paid out or received) occurring at regular intervals. As in
compound interest calculations, the interval between cash flows can be any time
period; however, the amounts of these cash flows need not be equal.
To understand how to use l and L, let’s consider the cash flow diagram for
an investment that requires an initial cash outlay (CF
0
) and generates a cash flow
(CF
1
) at the end of the first year, and so on up to the final cash flow (CF
6
) at the
end of the sixth year. In the following diagram, the initial investment is denoted
by CF
0
, and is depicted as an arrow pointing down from the time line since it is
cash paid out. Cash flows CF
1
and CF
4
also point down from the time line,
because they represent projected cash flow losses.
NPV is calculated by adding the initial investment (represented as a negative
cash flow) to the present value of the anticipated future cash flows. The interest
rate, i, will be referred to in this discussion of NPV and IRR as the rate of
return.
14
The value of NPV indicates the result of the investment.
z If NPV is positive, the financial value of the investors assets would be
increased: the investment is financially attractive.
z If NPV is zero, the financial value of the investors assets would not
change: the investor is indifferent toward the investment.
z If NPV is negative, the financial value of the investors assets would be
decreased: the investment is not financially attractive.
14.
Other terms are sometimes used to refer to the rate of return. These include: required rate of
return, minimally acceptable rate of return, and cost of capital.
Section 4: Additional Financial Functions 59
A comparison of the NPVs of alternative investment possibilities indicates
which of them is most desirable: the greater the NPV, the greater the increase in
the financial value of the investors assets.
IRR is the rate of return at which the discounted future cash flows equal the
initial cash outlay: IRR is the discount rate at which NPV is zero. The value of
IRR relative to the present value discount rate also indicates the result of the
investment:
z If IRR is greater than the desired rate of return, the investment is
financially attractive.
z If IRR is equal to the desired rate of return, the investor is indifferent
toward the investment.
z If IRR is less than the desired rate of return, the investment is not
financially attractive.
Calculating Net Present Value (NPV)
Calculating NPV for Ungrouped Cash Flows. If there are no equal
consecutive cash flows, use the procedure described (and then summarized)
below. With this procedure, NPV (and IRR) problems involving up to 30 cash
flows (in addition to the initial investment CF
0
) can be solved. If two or more
consecutive cash flows are equal – for example, if the cash flows in periods three
and four are both $8,500 – you can solve problems involving more than 30 cash
flows, or you can minimize the number of storage registers required for
problems involving less than 30 cash flows, by using the procedure described
next (under Calculating NPV for Grouped Cash Flows, page 61).
The amount of the initial investment (CF
0
) is entered into the calculator using
the J key.
Each cash flow (CF
1
, CF
2
, etc.) is designated CF
j
, where j takes on values from
1 up to the number of the final cash flow. The amount of a cash flow is entered
using the K key. Each time gK is pressed, the amount in the display is
stored in the next available storage register, and the number in the n register is
increased by 1. This register therefore counts how many cash flow amounts (in
addition to the initial investment CF
0
) have been entered.
Note: When entering cash flow amounts – including the initial investment
CF
0
– remember to observe the cash flow sign convention by pressing
Þ after keying in a negative cash flow.
In summary, to enter the cash flow amounts:
1. Press fCLEARH to clear the financial and storage registers.
60 Section 4: Additional Financial Functions
2. Key in the amount of the initial investment, press Þ if that cash flow is
negative, then press gJ. If there is no initial investment, press 0
gJ.
3. Key in the amount of the next cash flow, press Þ if the cash flow is
negative, then press gK. If the cash flow amount is zero in the next
period, press 0 gK.
4. Repeat step 3 for each cash flow until all have been entered.
With the amounts of the cash flows stored in the calculators registers, you can
calculate NPV as follows:
1. Enter the interest rate, using ¼ or C.
2. Press fl.
The calculated value of NPV appears in the display and also is automatically
stored in the PV register.
Example: An investor has an opportunity to buy a duplex for $80,000 and would
like a return of at least 13%. He expects to keep the duplex 5 years and then sell
it for $130,000; and he anticipates the cash flows shown in the diagram below.
Calculate NPV to determine whether the investment would result in a return or a
loss.
Note that although a cash flow amount ($4,500) occurs twice, these cash flows
are not consecutive. Therefore, these cash flows must be entered using the
method described above.
Keystrokes Display
fCLEARH
0.00
Clears financial and storage
registers.
80000ÞgJ
–80,000.00
Stores CF
0
(with minus sign for a
negative cash flow).
500ÞgK
–500.00
Stores CF
1
(with minus sign for a
negative cash flow).
Section 4: Additional Financial Functions 61
Since NPV is positive, the investment would increase the financial value of the
investors assets.
Calculating NPV for Grouped Cash Flows. A maximum of 30 cash flow
amounts (in addition to the initial investment CF
0
) can be stored in the HP 12C
Platinum.
15
However, problems involving more than 30 cash flows can be
handled if among the cash flows there are equal consecutive cash flows. For such
problems, you merely enter along with the amounts of the cash flows the number
of times – up to 99 – each amount occurs consecutively. This number is
designated N
j
, corresponding to cash flow amount CF
j
, and is entered using the
a key. Each N
j
is stored in a special register inside the calculator.
This method can, of course, be used for problems involving fewer than 30 cash
flows – and it will require fewer storage registers than the method described
above under Calculating NPV for Ungrouped Cash Flows. Equal consecutive
cash flows can be entered using that method – provided there are enough storage
registers available to accommodate the total number of individual cash flows.
The facility of grouping equal consecutive cash flows is provided to minimize
the number of storage registers required.
Note: When entering cash flow amounts – including the initial investment
CF
0
– remember to observe the cash flow sign convention by pressing
Þ after keying in the amount for a negative cash flow.
In summary, to enter the amounts of the cash flows and the number of times they
occur consecutively:
1. Press fCLEARH to clear the financial and storage registers.
2. Key in the amount of the initial investment, press Þ if that cash flow is
negative, then press gJ. If there is no initial investment, press
0gJ.
4500gK
4,500.00
Stores CF
2
.
5500gK
5,500.00
Stores CF
3
.
4500gK
4,500.00
Stores CF
4
.
130000gK
130,000.00
Stores CF
5
.
:n
5.00
Checks number of cash flow
amounts entered (in addition to
CF
0
.
13¼
13.00
Stores i.
fl
212.18
NPV.
15.
If you have stored a program in the calculator, the number of registers available for storing
cash flow amounts may be less than 31.
Keystrokes (Cont.) Display
62 Section 4: Additional Financial Functions
3. If the initial investment consists of more than one cash flow of the amount
entered in step 2, key in the number of those cash flows, then press ga.
If ga is not pressed, the calculator assumes that N
0
is 1.
4. Key in the amount of the next cash flow, press Þ if that cash flow is
negative, then press gK. If the cash flow amount is zero in the next
period, press 0gK.
5. If the amount entered in step 4 occurs more than once consecutively, key in
the number of times that cash flow amount occurs consecutively, then
press ga. If ga is not pressed, the calculator assumes that N
j
is 1
for the CF
j
just entered.
6. Repeat steps 4 and 5 for each CF
j
and N
j
until all cash flows have been
entered.
With the amounts of the cash flows and the number of times they occur
consecutively stored in the calculator, NPV can be calculated by entering the
interest rate and pressing fl, just as described earlier.
Example: An investor has an opportunity to purchase a piece of property for
$79,000; and he would like a 13½% return. He expects to be able to sell it after
10 years for $100,000 and anticipates the yearly cash flows shown in the table
below:
Since two cash flow amounts ($10,000 and $9,000) are repeated consecutively,
we can minimize the number of storage registers required by using the method
just described.
Year Cash Flow Year Cash Flow
1
2
3
4
5
$14,000
$11,000
$10,000
$10,000
$10,000
6
7
8
9
10
$9,100
$9,000
$9,000
$4,500
$100,000
Keystrokes Display
fCLEARH
0.00
Clears financial and storage
registers.
79000ÞgJ
–79,000.00
Initial investment (with minus sign
for a negative cash flow).
14000gK
14,000.00
First cash flow amount
11000gK
11,000.00
Next cash flow amount.
10000gK
10,000.00
Next cash flow amount.
Section 4: Additional Financial Functions 63
Since NPV is positive, the investment would increase the financial value of the
investors assets by $907.77.
Calculating Internal Rate of Return (IRR)
1. Enter the cash flows using either of the methods described above under
Calculating Net Present Value.
2. Press fL.
The calculated value of IRR appears in the display and also is automatically
stored in the i register.
Note: Remember that the L function may take a significant amount of
time to produce an answer, during which the calculator displays running.
Example: The NPV calculated in the preceding example was positive,
indicating that the actual rate of return (that is, the IRR) was greater than the
13½% used in the calculation. Find the IRR.
Assuming the cash flows are still stored in the calculator, we need only press
fL:
Note that the value calculated by L is the periodic rate of return. If the cash
flow periods are other than years (for example, months or quarters), you can
calculate the nominal annual rate of return by multiplying the periodic IRR by
the number of periods per year.
As noted above, the calculator may take several seconds or even minutes to
produce an answer for IRR. This is because the mathematical calculations for
3ga
3.00
Number of times this cash flow
amount occurs consecutively.
9100gK
9,100.00
Next cash flow amount.
9000gK
9,000.00
Next cash flow amount.
2ga
2.00
Number of times this cash flow
amount occurs consecutively.
4500gK
4,500.00
Next cash flow amount.
100000gK
100,000.00
Final cash flow amount.
:n
7.00
Seven different cash flow amounts
have been entered.
13.5¼
13.50
Stores i.
fl
907.77
NPV
Keystrokes Display
fL
13.72
IRR is 13.72%.
Keystrokes Display
64 Section 4: Additional Financial Functions
finding IRR are extremely complex, involving a series of iterations – that is, a
series of successive calculations. In each iteration, the calculator uses an estimate
of IRR as the interest rate in a computation of NPV. The iterations are repeated
until the computed NPV reaches about zero.
16
If you do not want to wait for the computation of IRR to be completed, press any
key. This halts the computation of IRR and displays the estimated value of IRR
being used in the current iteration.
17
You can then check how good this estimate
is by calculating NPV using this estimate: if the estimate is close to IRR, the NPV
calculated with it should be close to zero.
18
The value of IRR is put into the i
register at the end of each iteration. Therefore, to check how good an estimate of
IRR is after that estimate is in the display, just press fl.
The complex mathematical characteristics of the IRR computation have an
additional ramification: Depending on the magnitudes and signs of the cash
flows, the computation of IRR may have a single answer, multiple answers, a
negative answer or no answer.
18
For additional information regarding L, refer to Appendix C. For an
alternative method of calculating IRR, refer to Section 13.
Reviewing Cash Flow Entries
z To display a single cash flow amount, press :, then key in the number
of the register containing the cash flow amount to be displayed.
Alternatively, store the number of that cash flow amount (that is, the value
of j for the CF
j
desired) in the n register, then press :gK.
z To review all the cash flow amounts, press :gK repeatedly. This
displays the cash flow amounts in reverse order – that is, beginning with
the final cash flow and proceeding to CF
0
.
z To display the number of times a cash flow amount occurs consecutively –
that is, to display the N
j
for a CF
j
store the number of that cash flow
amount (that is, the value of j) in the n register, then press :ga.
z To review all the cash flow amounts together with the number of times
each cash flow amount occurs consecutively (that is, to review each CF
j
and N
j
pair), press :ga:gK repeatedly. This displays N
j
followed by CF
j
beginning with the final cash flow amount and proceeding
to N
0
and CF
0
.
16.
In practice, because the complex mathematical calculations inside the calculator are done
with numbers rounded to 10 digits, NPV may never reach exactly zero. Nevertheless, the
interest rate that results in a very small NPV is very close to the actual IRR.
17.
Provided the first iteration has been completed.
18.
In the case of multiple answers for IRR, the decision criteria listed on page 58 should be
modified accordingly.
Section 4: Additional Financial Functions 65
Note: Neither L nor l change the number in the n register. However,
each time :gK is pressed, the number in the n register is decreased
by 1. If this is done, or if you manually change the number in the n register
in order to display a single N
j
and/or CF
j
, be sure to reset the number in the
n register to the total number of cash flow amounts originally entered (not
including the amount of the initial investment CF
0
). If this is not done,
NPV and IRR calculations will give incorrect results; also, a review of cash
flow entries would begin with N
n
and CF
n
, where n is the number currently
in the n register.
For example, to display the fifth cash flow amount and the number of times that
amount occurs consecutively:
To display all the cash flow amounts and the number of times they occur
consecutively:
Keystrokes Display
:5
9,000.00
CF
5
5n
5.00
Stores the value of j in the n
register.
:ga
2.00
N
5
7n
7.00
Resets the number in the n register
to its original value.
Keystrokes Display
:ga
1.00
N
7
:gK
100,000.00
CF
7
:ga
1.00
N
6
:gK
4,500.00
CF
6
:ga
2.00
N
5
:gK
9,000.00
CF
5
.
.
.
.
.
.
.
.
.
:ga
1.00
N
1
:gK
14,000.00
CF
1
:ga
1.00
N
0
:gK
–79,000.00
CF
0
7n
7.00
Resets the number in the n register
to its original value.
66 Section 4: Additional Financial Functions
Changing Cash Flow Entries
z To change a cash flow amount:
1. Key the amount into the display.
2. Press ?.
3. Key in the number of the register containing the cash flow amount to be
changed.
z To change the number of times a cash flow amount occurs consecutively –
that is, to change the N
j
for a CF
j
:
1. Store the number of that cash flow amount (that is, j) in the n register.
2. Key the number of times the cash flow amount occurs consecutively
into the display.
3. Press ga.
Note: If you change the number in the n register in order to change an N
j
,
be sure to reset the number in the n register to the total number of cash
flow amounts originally entered (not including the amount of the initial
investment CF
0
). If this is not done, NPV and IRR calculations will give
incorrect results.
Example 1: With the cash flows now stored in the calculator, change CF
2
from
$11,000 to $9,000, then calculate the new NPV for a 13½% return.
Since this NPV is negative, the investment would decrease the financial value of
the investors assets.
Example 2: Change N
5
from 2 to 4, then calculate the new NPV.
Keystrokes Display
9000?2
9,000.00
Stores the new CF
2
in R
2
.
13.5¼
13.50
Stores i
a
a This step is necessary in this example because we have calculated IRR since the first
time we calculated NPV. The IRR calculation replaced the 13.5 we keyed into i before
calculating NPV with the result for IRR – 13.72.
fl
–644.75
The new NPV.
Keystrokes Display
5n
5.00
Stores j in the n register.
4ga
4.00
Stores the new N
5
.
7n
7.00
Resets the number in the n register
to its original value.
fl
–1,857.21
The new NPV.
Section 4: Additional Financial Functions 67
Bond Calculations
The HP 12C Platinum enables you to solve for bond price (and the interest
accrued since the last interest date) and the yield to maturity.
19
The E and
S calculations are done assuming a semiannual coupon payment and using an
actual/actual basis (such as for U.S. Treasury bonds and U.S. Treasury notes). In
accordance with market convention, prices are based on a redemption (par) value
of 100.
To calculate bond price and yield for a 30/360 bond (that is, using the basis of a
30-day month and a 360-day year – such as for municipal bonds, corporate
bonds, and state and local government bonds), and to calculate bond price for
bonds with an annual coupon payment, refer to Section 16: Bonds.
Bond Price
1. Enter the desired yield to maturity (as a percentage), using ¼.
2. Enter the annual coupon rate (as a percentage), using P.
3. Key in the settlement (purchase) date (as described on page 30), then press
\.
4. Key in the maturity (redemption) date.
5. Press fE.
The price is shown in the display and also is stored in the PV register. The
interest accrued since the last interest date is held inside the calculator: to display
the interest, press ~; to add the interest to the price, press +.
Example: What price should you pay on April 28, 2003 for a 6¾% U.S.
Treasury bond that matures on June 4, 2017, if you want a yield of 8¼%.
Assume that you normally express dates in the month-day-year format.
19.
All bond calculations are performed in accordance with. the Securities Industry Association’s
recommendations as contained in Spence, Graudenz, and Lynch, Standard Securities
Calculation Methods, Securities Industry Association, New York, 1973.
Keystrokes (RPN mode) Display
8.25¼
8.25
Enters yield to maturity.
6.75P
6.75
Enters coupon rate.
6.75
Sets date format to month-day-year.
4.282003\
4.28
Enters settlement (purchase) date.
6.042017
6.042017
Enters maturity (redemption) date.
fE
87.62
Bond price (as a percent of par).
+
90.31
Total price, including accrued
interest.
68 Section 4: Additional Financial Functions
Bond Yield
1. Enter the quoted price (as a percent of par), using $.
2. Enter the annual coupon rate (as a percentage), using P.
3. Key in the settlement (purchase) date, then press \.
4. Key in the maturity (redemption) date.
5. Press fS.
The yield to maturity is shown in the display and also is stored in the i register.
Note: Remember that the S function may take a significant amount of
time to produce an answer, during which the calculator displays running.
Example: The market is quoting 88
3
/8% for the bond described in the preceding
example. What yield will that provide?
Depreciation Calculations
The HP 12C Platinum enables you to calculate depreciation and the remaining
depreciable value (book value minus salvage value) using the straight-line,
sum-of-the-years-digits, and declining-balance methods. To do so with any of
these methods:
1. Enter the original cost of the asset, using $.
2. Enter the salvage value of the asset, using M. If the salvage value is zero,
press 0M.
3. Enter the expected useful life of the asset (in years), using n.
4. If the declining-balance method is being used, enter the declining-balance
factor (as a percentage), using ¼. For example, 1¼ times the straight-line
rate – 125 percent declining-balance – would be entered as 125¼.
5. Key in the number of the year for which depreciation is to be calculated.
Keystrokes (RPN mode) Display
3\8z
0.38
Calculates
3
/8.
88+$
88.38
Enters quoted price.
6.75P
6.75
Enters coupon rate.
4.282003\
4.28
Enters settlement (purchase) date.
6.042017
6.042017
Enters maturity (redemption) date.
fS
8.15
Bond yield
Section 4: Additional Financial Functions 69
6. Press:
z fV for depreciation using the straight-line method.
z for depreciation using the sum-of-the-years digits method.
z f# for depreciation using the declining-balance method.
V, Ý, and # each place the amount of depreciation in the display. To
display the remaining depreciable value (the book value less the salvage value)
after the depreciation has been calculated, press ~.
Example: A metalworking machine, purchased for $10,000, is depreciated over
5 years. Its salvage value is estimated at $500. Find the depreciation and
remaining depreciable value for the first 3 years of the machine’s life using the
declining-balance method at double the straight-line rate (200 percent
declining-balance).
To calculate depreciation and the remaining depreciable value when the
acquisition date of the asset does not coincide with the beginning of the fiscal
accounting year, refer to the procedures in Section 13. That section also includes
a procedure for depreciation calculations when changing from the
declining-balance method to the straight-line method, and a procedure for
calculating excess depreciation.
Keystrokes Display
10000$
10,000.00
Enters original cost.
500M
500.00
Enters salvage value.
5n
5.00
Enters expected useful life.
200¼
200.00
Enters declining-balance factor.
1f#
4,000.00
Depreciation in first year.
~
5,500.00
Remaining depreciable value after
first year.
2f#
2,400.00
Depreciation in second year.
~
3,100.00
Remaining depreciable value after
second year.
3f#
1,440.00
Depreciation in third year.
~
1,660.00
Remaining depreciable value after
third year.
70 Section 5: Additional Operating Features
Section 5
Additional Operating Features
Continuous Memory
The calculators Continuous Memory contains the data storage registers, the
financial registers, the stack and LAST X registers, program memory, and status
information such as display format, date format, and payment mode. All
information in Continuous Memory is preserved even while the calculator is
turned off. Furthermore, information in Continuous Memory is preserved for a
short time when the batteries are removed, so that you can change the batteries
without losing your data and programs.
Continuous Memory may be reset if the calculator is dropped or otherwise
traumatized, or if power is interrupted. You can also manually reset Continuous
Memory as follows:
1. Turn the calculator off.
2. Hold down the - key, and press ;.
When Continuous Memory is reset:
z All registers are cleared.
z Program memory consists of eight program lines, each containing the
instruction g(000.
z Display format is set to the standard format with two decimal places.
z Date format is set to month-day-year.
z Payment mode is set to End.
Whenever Continuous Memory has been reset, the display will show Pr Error.
Pressing any key will clear this message from the display.
The Display
Status Indicators
Eight indicators that appear along the bottom of the display signify the status of
the calculator for certain operations. These status indicators are described
elsewhere in this handbook where the relevant operation is discussed.
RPN ALG f g BEGIN D.MY C PRGM
Section 5: Additional Operating Features 71
Number Display Formats
When the calculator is first turned on after coming from the factory or after
Continuous Memory has been reset, answers are displayed with two decimal
places.
Although you see only two decimal places, all calculations in your HP 12C
Platinum are performed with full 10-digit numbers.
When only two decimal places are displayed, numbers are rounded to two
decimal places: if the third digit is 5 through 9, the second digit is increased by
one; if the third digit is 0 through 4, the second digit is not affected. Rounding
occurs regardless of how many decimal places are displayed.
Several options are provided for controlling how numbers appear in the display.
But regardless of which display format or how many displayed decimal places
you specify, the number inside the calculator – which appears altered in the
display – is not altered unless you use the B, !, V, Ý, or #
functions.
Standard Display Format. The number 14.87 now in your calculator is
currently being displayed in the standard display format with two decimal places
shown. To display a different number of decimal places, press f followed by a
digit key (0 through 9) specifying the number of decimal places. In the following
examples, notice how the displayed form of the number inside the calculator –
14.87456320 – is rounded to the specified number of digits.
Keystrokes (RPN mode) Display
19.8745632\
19.87
5-
14.87
72 Section 5: Additional Operating Features
The standard display format, plus the specified number of decimal places,
remain in effect until you change them; they are not reset each time the
calculator is turned on. However, if Continuous Memory is reset, when the
calculator is next turned on numbers will be displayed in the standard display
format with two decimal places shown.
If a calculated answer is either too small or too large to be displayed in the
standard display format, the display format automatically switches to scientific
notation (described below). The display returns to the standard display format
for all numbers that can be displayed in that format.
Scientific Notation Display Format
In scientific notation, a number is displayed with its mantissa at the left and a
two-digit exponent at the right. The mantissa is simply the first seven digits in
the number, and has a single, nonzero digit to the left of the decimal point. The
exponent is simply how many decimal places you would move the decimal point
in the mantissa before writing down the number in standard format. If the
exponent is negative (that is, there is a minus sign between it and the mantissa),
the decimal point should be moved to the left; this occurs for any number less
than 1. If the exponent is positive (that is, there is a blank space between it and
the mantissa), the decimal point should be moved to the right; this occurs for any
number greater than or equal to 1.
Keystrokes Display
f4
14.8746
f1
14.9
f0
15.
f9
14.87456320
Although nine decimal places were
specified after f, only eight are
displayed since the display can
show a total of only 10 digits.
Section 5: Additional Operating Features 73
To set the display format to scientific notation, press f.. For example
(assuming the display still shows 14.87456320 from the preceding example):
The exponent in this example indicates that the decimal point should be moved
one decimal place to the right, giving the number 14.87456, which is the first
seven digits of the number previously in the display.
To set the display back to standard display format, press f followed by the
desired number of decimal places. Scientific notation display format remains in
effect until you change to the standard display format; it is not reset each time the
calculator is turned on. However, if Continuous Memory is reset, when the
calculator is next turned on the standard display format, with two decimal places,
will be used.
Mantissa Display Format. Because both the standard display format and
scientific notation display format often show only a few digits of a number, you
may occasionally want to see all 10 digits – the full mantissa – of the number
inside the calculator. To do so, press fCLEAR X and hold down the X
key. The display will show all 10 digits of the number as long as you hold down
the X key; after you release the key, the number will again be displayed in the
current display format. For instance, if the display still contains the result from
the preceding example:
Special Displays
Running. Certain functions and many programs may take several seconds or
more to produce an answer. During these calculations, the word running flashes
in the display to let you know that the calculator is running.
Overflow and Underflow. If a calculation results in a number whose magnitude
is greater than 9.999999999 × 10
99
, the calculation is halted and the calculator
displays 9.999999 99 (if the number is positive) or –9.999999 99 (if the
number is negative).
Keystrokes Display
f.
1.487456 01
Keystrokes Display
fCLEAR X
1487456320
All 10 digits of the number inside
the calculator.
1.487456 01
Display returns to its former
contents when the X key is
released.
f2
14.87
Returns display to standard format.
74 Section 5: Additional Operating Features
If a calculation results in a number whose magnitude is less than 10-
99
, the
calculation is not halted, but the value 0 is used for that number in subsequent
calculations.
Errors. If you attempt an improper operation – such as division by zero – the
calculator will display the word Error followed by a digit (0 through 9). To clear
the Error display, press any key. This does not execute that key’s function, but
does restore the calculator to its condition before the improper operation was
attempted. Refer to Appendix D for a list of error conditions.
Pr Error. If power to the calculator is interrupted, the calculator will display Pr
Error when next turned on. This indicates that Continuous Memory – which
contains all data, program, and status information – has been reset.
The ~ Key
Suppose you need to subtract $25.83 from $144.25, and you (mistakenly) key in
25.83, press \, then key in 144.25. But then you realize that when written
down on paper, the desired calculation reads 144.25 – 25.83, so that you have
unfortunately keyed in the second number first. To correct this mistake, merely
exchange the first and second numbers by pressing ~, the exchange key.
The ~ key is also useful for checking the first number entered to make sure
you keyed it in correctly. Before pressing the operation key, however, you should
press ~ again to return the second number entered to the display. Regardless
of how many times you press ~, the calculator considers the number in the
display to be the second number entered.
The F Key
Occasionally you may want to recall to the display the number that was there
before an operation was performed. (This is useful for doing arithmetic
calculations with constants and for recovering from errors in keying in numbers.)
To do so, press gF (last x).
Keystrokes (RPN mode) Display
25.83\144.25
144.25
Oops! You mistakenly keyed in the
second number first.
~
25.83
Exchanges the first and second
numbers. The first number keyed in
is now in the display.
-
118.42
The answer is obtained by pressing
the operation key.
Section 5: Additional Operating Features 75
Arithmetic Calculations With Constants
Example: At Permex Pipes a certain pipe fitting is packaged in quantities of 15,
75, and 250. If the cost per fitting is $4.38, calculate the cost of each package.
Another method for doing arithmetic calculations with constants is described on
page 173.
Recovering From Errors in Digit Entry
Example: Suppose you want to divide the total annual production for one of
your firm’s products (429,000) by the number of retail outlets (987) in order to
calculate the average number distributed by each outlet. Unfortunately, you
mistakenly key in the number of outlets as 9987 rather than as 987. It’s easy to
correct:
Keystrokes (RPN mode) Display
15\
15.00
Keys first quantity into calculator.
4.38
4.38
Keys unit cost into display.
§
65.70
Cost of a package of 15.
75
75.
Keys second quantity into display.
gF
4.38
Recalls unit cost – which was last
number in display before § was
pressed – into display.
§
328.50
Cost of a package of 75.
250
250.
Keys third quantity into display.
gF
4.38
Recalls unit cost into display again.
§
1,095.00
Cost of a package of 250.
Keystrokes (RPN mode) Display
429000\
429,000.00
9987
9,987.
You haven’t noticed your mistake
yet.
z
42.96
About 43 products per outlet – but
that seems too low!
gF
9,987.00
Recalls to the display the number
that was there before you press z.
You see that you keyed it in wrong.
429000\
429,000.00
Begins the problem over.
987z
434.65
The correct answer.
76
Section 6
Statistics Functions
Accumulating Statistics
The HP 12C Platinum can perform one- or two-variable statistical calculations.
The data is entered into the calculator using the _ key, which automatically
calculates and stores statistics of the data into storage registers R
1
, through R
6
.
(These registers are therefore referred to as the “statistics registers.”)
Before beginning to accumulate statistics for a new set of data, you should clear
the statistics registers by pressing fCLEAR².
20
In one-variable statistical calculations, to enter each data point – referred to as an
x-value” – key the x-value into the display, then press _.
In two-variable statistical calculations, to enter each data pair – referred to as the
x- and y-values”:
1. Key the y-value into the display.
2. Press \.
3. Key the x-value into the display.
4. Press _.
Each time you press _, the calculator does the following:
z The number in R
1
is increased by 1, and the result is copied into the
display.
z The x-value is added to the number in R
2
.
z The square of the x-value is added to the number in R
3
.
z The y-value is added to the number in R
4
.
z The square of the y-value is added to the number in R
5
.
z The product of the x- and y-values is added to the number in R
6
.
The table below shows where the accumulated statistics are stored.
20.
This also clears the stack registers and the display.
Section 6: Statistics Functions 77
Correcting Accumulated Statistics
If you discover you have entered data incorrectly, the accumulated statistics can
easily be corrected:
z If the incorrect data point or data pair has just been entered and _ has
been pressed, press gFg^.
z If the incorrect data point or data pair is not the most recent one entered,
key in the incorrect data point or data pair again as if it were new, but press
g^ instead of _.
These operations cancel the effect of the incorrect data point or data pair. You
can then enter the data correctly, using _, just as if it were new.
Mean
Pressing calculates the means (arithmetic averages) of the x-values ( )
and of the y-values ( ). The mean of the x-values appears in the display after Ö
is pressed; to display the mean of the y-values, press ~.
Example: A survey of seven salespersons in your company reveals that they
work the following hours a week and sell the following dollar volumes each
month. How many hours does the average salesperson work each week? How
much does the average salesperson sell each month?
Register Statistic
R
1
(and display) n: number of data pairs accumulated.
R
2
Σx: summation of x-values.
R
3
Σx
2
: summation of squares of
x-values.
R
4
Σy: summation of y-values.
R
5
Σy
2
summation of squares of y-values.
R
6
Σxy: summation of products of
x-values and y-values.
x
y
78 Section 6: Statistics Functions
To find the average workweek and sales of this sample:
Standard Deviation
Pressing gv calculates the standard deviation of the x-values (s
x
) and of the
y-values (s
y
). (The standard deviation of a set of data is a measure of the
dispersion around the mean.) The standard deviation of the x-values appears in
the display after v is pressed; to display the standard deviation of the y-values,
press ~.
Salesperson Hours/Week Hours/Week
132$17,000
240$25,000
345$26,000
440$20,000
538$21,000
650$28,000
735$15,000
Keystrokes Display
fCLEAR²
00.00
Clears statistics registers.
32\
17000_
32.00
1.00
First entry.
40\
25000_
40.00
2.00
Second entry.
45\
26000_
45.00
3.00
Third entry.
40\
20000_
40.00
4.00
Fourth entry.
38\
21000_
38.00
5.00
Fifth entry.
50\
28000_
50.00
6.00
Sixth entry.
35\
15000_
35.00
7.00
Total number of entries in the
sample.
21,714.29
Mean dollar sales per month ( ).
~
40.00
Mean workweek in hours ( ).
x
y
Section 6: Statistics Functions 79
Example: To calculate the standard deviations of the x-values and of the
y-values from the preceding example:
The formulas used in the HP 12C Platinum for calculating s
x
, and s
y
give best
estimates of the population standard deviation based on a sample of the
population. Thus, current statistical convention calls them sample standard
deviations. So we have assumed that the seven salespersons are a sample of the
population of all salespersons, and our formulas derive best estimates of the
population from the sample.
What if the seven salespersons constituted the whole population of salespersons.
Then we wouldn’t need to estimate the population standard deviation. We can
find the true population standard deviation (σ) when the data set equals the total
population, using the following keystrokes.
21
To continue summing data pairs, press gÖg^ before entering more data.
Linear Estimation
With two-variable statistical data accumulated in the statistics registers, you can
estimate a new y-value ( ) given a new x-value, and estimate a new x-value ( )
given a new y-value.
To calculate :
1. Key in a new x-value.
2. Press gR.
To calculate :
1. Key in a new y-value.
2. Press gQ.
Keystrokes Display
gv
4,820.59
Standard deviation of sales.
~
6.03
Standard deviation of hours worked.
Keystrokes Display
21,714.29
Mean (dollars)
_
8.00
Number of entries + 1.
gv
4,463.00
σ
x
~
5.58
σ
y
21.
It turns out that if you sum the mean of the population into the set itself and find the new s,
computed using the formulas on page 192, that s will be the population standard deviation, σ,
of the original set.
y
ˆ
x
ˆ
y
ˆ
x
ˆ
80 Section 6: Statistics Functions
Example: Using the accumulated statistics from the preceding problem,
estimate the amount of sales delivered by a new salesperson working 48 hours
per week.
The reliability of a linear estimate depends upon how closely the data pairs
would, if plotted on a graph, lie in a straight line. The usual measure of this
reliability is the correlation coefficient, r. This quantity is automatically
calculated whenever or is calculated; to display it, press ~. A correlation
coefficient close to 1 or –1 indicates that the data pairs lie very close to a straight
line. On the other hand, a correlation coefficient close to 0 indicates that the data
pairs do not lie closely to a straight line; and a linear estimate using this data
would not be very reliable.
Example: Check the reliability of the linear estimate in the preceding example
by displaying the correlation coefficient.
To graph the regression line, calculate the coefficients of the linear equation
y = A + Bx.
1. Press 0gR to compute the y-intercept (A).
2. Press 1gR~d~- to compute the slope of the line (B).
Example: Compute the slope and intercept of the regression line in the
preceding example.
The equation that describes the regression line is:
y = 15.55 + 0.001x
Keystrokes Display
48gQ
28,818.93
Estimated sales for a 48 hour
workweek.
Keystrokes Display
~
0.90
The correlation coefficient is close
to 1, so the sales calculated in the
preceding example is a good
estimate.
Keystrokes (RPN mode) Display
0gR
15.55
y-intercept (A); projected value for
x = 0.
1 gR~d~-
0.001
Slope of the line (B); indicates the
change in the projected values
caused by an incremental change in
the x value.
y
ˆ
x
ˆ
Section 6: Statistics Functions 81
Weighted Mean
You can compute the weighted mean of a set of numbers if you know the
corresponding weights of the items in question.
1. Press fCLEAR².
2. Key in the value of the item and press \, then key in its weight and
press _. Key in the second item’s value, press \, key in the second
weight, and press _. Continue until you have entered all the values of the
items and their corresponding weights. The rule for entering the data is
“item \ weight _.”
3. Press gh to calculate the weighted mean of the items.
Example: Suppose that you stop during a vacation drive to purchase gasoline at
four stations as follows: 15 gallons at $1.16 per gallon, 7 gallons at $1.24 per
gallon, 10 gallons at $1.20 per gallon, and 17 gallons at $1.18 per gallon. You
want to find the average cost per gallon of gasoline purchased. If you purchased
the same quantity at each station, you could determine the simple arithmetic
average or mean using the Ö key. But since you know the value of the item
(gasoline) and its corresponding weight (number of gallons purchased), use the
h key to find the weighted mean:
A procedure for calculating the standard deviation and standard error (as well as
the mean) of weighted or grouped data is included in the HP 12C Platinum
Solutions Handbook.
Keystrokes Display
fCLEAR²
0.00
Clears statistics registers.
1.16\15_
1.00
First item and weight.
1.24\7_
2.00
Second item and weight.
1.20\10_
3.00
Third item and weight.
1.18\17_
4.00
Fourth item and weight.
gh
1.19
Weighted mean cost per gallon.
82
Section 7
Mathematics and
Number-Alteration Functions
The HP 12C Platinum provides several keys for mathematical functions and for
altering, numbers. These functions are useful for specialized financial
calculations as well as for general mathematics calculations.
One-Number Functions
Most of the mathematics functions require that only one number be in the
calculator (that is, the number in the display) before the function key is pressed.
Pressing the function key then replaces the number in the display by the result.
Reciprocal. Pressing y calculates the reciprocal of the number in the display –
that is, it divides 1 by the number in the display.
Square. Pressing g’ calculates the square of the number in the display.
Square Root. Pressing gr calculates the square root of the number in the
display.
Logarithm. Pressing g¿ calculates the natural logarithm (that is, the
logarithm to the base e) of the number in the display. To calculate the common
logarithm (that is, the logarithm to the base 10) of the number in the display,
calculate the natural logarithm, then press 10g¿z.
Exponential. Pressing g> calculates the exponential of the number in the
display – that is, it raises the base e to the number in the display.
Factorial. Pressing ge calculates the factorial of the number in the display –
that is, it calculates the product of the integers from 1 to n, where n is the number
in the display.
Round. The display format specifies to how many decimal places a number
inside the calculator is rounded when it appears in the display; but the display
format alone does not affect the number itself inside the calculator. Pressing
fB, however, changes the number inside the calculator to match its
displayed version. Thus, to round a number in the display to a given number of
decimal places, temporarily set the display format (as described on page 71) to
show the desired number of decimal places, then press fB.
Section 7: Mathematics and Number-Alteration Functions 83
Integer. Pressing replaces the number in the display by its integer
portion – that is, it replaces each digit to the right of the decimal point by 0. The
number is changed inside the calculator as well as in the display. The original
number can be recalled to the display by pressing gF.
Fractional. Pressing gT replaces the number in the display by its fractional
portion – that is, it replaces all digits to the left of the decimal point by 0. Like
Ñ, T changes the number inside the calculator as well as its displayed
version. The original number can be recalled to the display by pressing gF.
All of the above functions are used basically in the same way. For example, to
find the reciprocal of 0.258:
Any of the above functions can be done with a number in the display resulting
from a previous calculation, as well as with a number you have just keyed in.
Keystrokes Display
.258
0.258
Keys the number into the display.
y
3.88
The reciprocal of 0.258, the original
number.
Keystrokes (RPN mode) Display
fCLEAR X
3875968992
Displays all 10 digits of the number
inside the calculator.
3.88
Display returns to normal format
when X key is released.
fB
3.88
The number now in the display
appears the same as before, but …
fX
3880000000
Displaying all 10 digits of the
number inside the calculator shows
B has changed the number to
match its displayed version.
3.88
Display returns to normal format.
3.00
The integer portion of the number
previously displayed.
gF
3.88
Recalls the original number to the
display.
gT
0.88
The fractional portion of the
number previously displayed.
84 Section 7: Mathematics and Number-Alteration Functions
The Power Function
Pressing q calculates a power of a number – that is, y
x
. Like the arithmetic
function +, q requires two numbers:
1. Key in the base number (which is designated by the y on the key).
2. Press \ to separate the second number (the exponent) from the first (the
base).
3. Key in the exponent (which is designated by the x on the key).
4. Press q to calculate the power.
To Calculate Keystrokes (RPN mode) Display
2
1.4
2\1.4q
2.64
2
–1.4
2\1.4Þq
0.38
(–2)
3
2Þ\3q
–8.00
or 2
1/3
2\3yq
1.26
2
3
Part II
Programming
86
Section 8
Programming Basics
Why Use Programs?
A program is simply a sequence of keystrokes that is stored in the calculator.
Whenever you have to calculate with the same sequence of keystrokes several
times, you can save a great deal of time by incorporating these keystrokes in a
program. Instead of pressing all the keys each time, you press just one key to
start the program: the calculator does the rest automatically!
Creating a Program
Creating a program consists simply of writing the program, then storing it:
1. Write down the sequence of keystrokes that you would use to calculate the
quantity or quantities desired.
2. Press fs to set the calculator to Program mode. When the calculator
is in Program mode, functions are not executed when they are keyed in, but
instead are stored inside the calculator. The PRGM status indicator in the
display is lit when the calculator is in Program mode.
3. Press fCLEARÎ to erase any previous programs that may be stored
inside the calculator. If you want to create a new program without erasing a
program already stored, skip this step and proceed as described in Section
11, Multiple Programs.
4. Select the mode you want to use (by pressing f] or f[).
Note: Programs or steps created and saved in RPN mode can only be
executed in RPN mode, and programs or steps created and saved in ALG
mode can only be executed in ALG mode. (You can also create steps in
your program to switch to the appropriate mode.)
5. Key in the sequence of keystrokes that you wrote down in step 1. Skip the
beginning keystrokes that enter data, which would differ each time the
program is used.
Example: Your office supplies dealer is selling selected stock at 25% off. Create
a program that calculates the net cost of an item after the discount is subtracted
and the $5 handling charge is added.
First, we’ll manually calculate the net cost of an item listing for $200.
Section 8: Programming Basics 87
Next, set the calculator to Program mode and erase any program(s) already
stored:
Finally, press the keys that we used above to solve the problem manually. Do not
key in 200; this number will vary each time the program is used. Don’t be
concerned right now about what appears in the display as you press the keys;
we’ll discuss that later in this section.
Running a Program
To run (sometimes called “execute”) a program:
1. Press fs to set the calculator back to Run mode. If the calculator is
already in Run mode (that is, the PRGM status indicator in the display is
not lit), skip this step.
2. Key any required data into the calculator, just as if you were calculating
manually. When a program is run, it uses the data already keyed into the
display and the registers inside the calculator.
3. Press t to begin program execution.
Keystrokes (RPN mode) Display
200
200.
Keys in cost of item.
\
200.00
Separates cost of item from
percentage to be keyed in next.
25b
50.00
Amount of discount.
-
150.00
Price less discount.
5
5.
Handling charge.
+
155.00
Net cost (price less discount plus
handling charge).
Keystrokes (RPN mode) Display
fs
000,
Sets calculator to Program mode.
fCLEARÎ
000,
Clears program(s).
Keystrokes (RPN mode) Display
\
001, 36
2
002, 2
5
003, 5
b
004, 25
-
005, 30
5
006, 5
+
007, 40
88 Section 8: Programming Basics
Example: Run the program created above to calculate the net cost of a
typewriter listing for $625 and an executive chair listing for $159.
That’s all there is to creating and running simple programs! But if you want to
use programs frequently, you’ll want to know more about programming – such
as how to check what keystrokes are stored in program memory, how many
keystrokes can be stored in program memory, how to correct or otherwise
modify programs, how to skip keystrokes when running a program, and so on.
Before you can understand these aspects of programming, we need to briefly
discuss how keystrokes are treated by the calculator when they are stored in
Program mode and when they are executed in Run mode.
Program Memory
Keystrokes entered into the calculator in Program mode are stored in program
memory. Each digit, decimal point, or function key is called an instruction and is
stored in one line of program memory – usually referred to simply as a program
line. Keystroke sequences beginning with the f, g, ?, :, and i
prefix keys are considered to comprise a complete instruction and are stored in
only one program line.
When a program is run, each instruction in program memory is executed – that
is, the keystroke in that program line is performed, just as if you were pressing
the key manually – beginning with the current line in program memory and
proceeding sequentially with the higher-numbered program lines.
Whenever the calculator is in Program mode (that is, whenever the PRGM status
indicator in the display is lit), the display shows information about the program
line to which the calculator is currently set. At the left of the display is the
number of the program line within program memory. The remaining digits in the
display comprise a code that indicates what instruction has been stored in that
program line. No code is shown for program line 000, since no regular
instruction is stored there.
Keystrokes (RPN mode) Display
fs
155.00
Sets calculator to Run mode.
Display shows number previously
calculated.
f]
155.00
Sets RPN mode.
625
625.
Keys in price of typewriter.
t
473.75
Net cost of typewriter.
159
159.
Keys in list price of chair.
t
124.25
Net cost of chair.
Section 8: Programming Basics 89
Identifying Instructions in Program Lines
Each key on the HP 12C Platinum keyboard – except for the digit keys 0 through
9 – is identified by a two-digit “keycode” that corresponds to the key’s position
on the keyboard. The first digit in the keycode is the number of the key row,
counting from row 1 at the top; the second digit is the number of the key in that
row, counting from 1 for the first key in the row through 9 for the ninth key in the
row and 0 for the tenth key in the row. The keycode for each digit key is simply
the digit on the key. Thus, when you keyed the instruction b into program
memory, the calculator displayed
004, 25
This indicates that the key for the instruction in program line 004 is in the second
row on the keyboard and is the fifth key in that row: the b key. When you
keyed the instruction + into program memory, the calculator displayed
007, 40
This indicates that the key for the instruction in program line 007 is in the fourth
row on the keyboard and is the tenth key in that row: the + key. When you
keyed the digit 5 into program memory, the keycode displayed was only the
digit 5.
Since keystroke sequences beginning with f, g, ?, :, and i are
stored in only one program line, the display of that line would show the keycodes
for all the keys in the keystroke sequence.
Instruction Keycode
nnn, 43 26
?=1
nnn,44 40 1
gi000
nnn,43,33,000
2
=
hp 12c platinum
financial calculator
90 Section 8: Programming Basics
Displaying Program Lines
Pressing fs to set the calculator from Run mode to Program mode displays
the line number and keycode for the program line to which the calculator is
currently set.
Occasionally you’ll want to check several or all of the instructions stored in
program memory. The HP 12C Platinum enables you to review program
instructions either forward or backward through program memory:
z Pressing Ê (single step) while the calculator is in Program mode
advances the calculator to the next line in program memory, then displays
that line number and the keycode of the instruction stored there.
z Pressing (back step) while the calculator is in Program mode sets
the calculator back to the previous line in program memory, then displays
that line number and the keycode of the instruction stored there.
For example, to display the first two lines of the program now stored in program
memory, set the calculator to Program mode and press Ê twice:
Pressing does the reverse:
If either the Ê key or the Ü key is held down, the calculator displays all of
the lines in program memory. Press Ê again now, but this time hold it down
until program line 007 is displayed.
Keystrokes Display
fs
000,
Sets calculator to Program
mode and displays current line
of program memory
Ê
001, 36
Program line 001: \
Ê
002, 2
Program line 002: digit 2.
Keystrokes Display
001, 36
Program line 001.
000,
Program line 000.
Keystrokes Display
Ê
001, 36
Program line 001
.
.
.
.
.
.
(Release Ê)
007, 40
Program line 007
Section 8: Programming Basics 91
Program line 007 contains the last instruction you keyed into program memory.
However, if you press Ê again, you’ll see that this is not the last line stored in
program memory:
As you should now be able to tell from the keycodes displayed, the instruction in
program line 008 is gi000.
The i000 Instruction and Program Line 000
Whenever you run the program now stored in program memory, the calculator
executes the instruction in line 008 after executing the seven instructions you
keyed in. This i000 instruction – as its name implies – tells the calculator to
“go to” program line 000 and execute the instruction in that line. Although line
000 does not contain a regular instruction, it does contain a “hidden” instruction
that tells the calculator to halt program execution. Thus, after each time the
program is run, the calculator automatically goes to program line 000 and halts,
ready for you to key in new data and run the program again. (The calculator is
also automatically set to program line 000 when you press fs to set the
calculator from Program mode to Run mode.)
The i000 instruction was already stored in line 008 – in fact, in all program
lines – before you keyed in the program. If no instructions have been keyed into
program memory, if Continuous Memory is reset, or if fCLEARÎ is
pressed (in Program mode), the instruction i000 is automatically stored in
program lines 001 through 008. As you key each instruction into program
memory, it replaces the i000 instruction in that program line.
If your program should consist of exactly eight instructions, there would be no
i000 instructions remaining at the end of program memory. Nevertheless,
after such a program is executed the calculator automatically returns to program
line 000 and halts, just as if there were a i000 instruction following the
program.
If you key in more than eight instructions, program memory automatically
expands to accommodate the additional instructions.
Expanding Program Memory
If no instructions have been keyed into program memory, if Continuous Memory
has been reset, or if fCLEARÎ has been pressed (in Program mode),
Keystrokes Display
008,43,33,000
Program line 008
92 Section 8: Programming Basics
program memory consists of 8 program lines, and there are 20 storage registers
available for storage of data.
As you key in a 310th instruction, storage register R
0.9
is automatically converted
into seven new lines of program memory. The instruction you key in is stored in
program line 310, and the instruction i000 is automatically stored in
program lines 311 through 316.
Program memory is automatically expanded like this whenever another seven
instructions have been keyed into program memory – that is, when you key an
instruction into program line 317, 324, 331 etc. In each case, the additional
program lines made available are converted, seven lines at a time, from the last
available data storage register (whether or not data has been stored in that
register; if it has, it will be lost). Furthermore, the six new program lines
(following the 317th, 324th etc.) will each contain the instruction i000.
Section 8: Programming Basics 93
To determine at any time how many program lines (including those containing
i000) are currently in program memory and how many storage registers are
currently available for conversion to program lines or for data storage, press
gN (memory). The calculator will respond with a display like the following:
Up to 400 instructions can be stored in program memory. Doing so would
require the conversion of 56 data storage registers (because 400 = 8 + [56 × 7]),
leaving 7 storage registers – R
0
through R
6
– available for data storage.
If you find yourself creating long programs, you should create your programs so
that they don’t use up program lines unnecessarily, since program memory is
limited to 400 program lines. One way to minimize program length is to replace
numbers consisting of more than just one digit – like the number 25 in lines 002
and 003 of the program keyed in above – by a : instruction, and then storing
the number in the designated storage register before running the program. In this
case, this would save one program line, since the : instruction requires only
one program line, not two as are required by the number 25. Of course, doing so
uses up data storage registers that you might want to save for other data. As in
many business and financial decisions, there is a trade off involved; here it is
between program lines and data storage registers.
Setting the Calculator to a Particular Program Line
There will be occasions when you’ll want to set the calculator directly to a
particular program line – such as when you’re storing a second program in
program memory or when you’re modifying an existing program. Although you
can set the calculator to any line by using Ê as described above, you can do so
more quickly as follows:
z With the calculator in Program mode, pressing gi. followed by
three digit keys sets the calculator to the program line specified by the digit
keys, and then displays that line number and the keycode of the instruction
stored there.
z With the calculator in Run mode, pressing gi followed by three digit
keys sets the calculator to the program line specified by the digit keys.
Since the calculator is not in Program mode, the line number and keycode
are not displayed.
The decimal point is not necessary if the calculator is in Run mode, but it is
necessary if the calculator is in Program mode.
94 Section 8: Programming Basics
For example, assuming the calculator is still in Program mode, you can set it to
program line 000 as follows:
Executing a Program One Line at a Time
Pressing Ê repeatedly with the calculator in Program mode (as described
earlier) enables you to verify that the program you have stored is identical to the
program you wrote – that is, to verify that you have keyed the instructions in
correctly. However, this does not ensure that the program you wrote calculates
the desired results correctly: even programs created by the most experienced
programmers often do not work correctly when they are first written.
To help you verify that your program works correctly, you can execute the
program one line at a time, using the Ê key. Pressing Ê while the calculator
is in Run mode advances the calculator to the next line in program memory, then
displays that line’s number and the keycode of the instruction stored there, just as
in Program mode. In Run mode, however, when the Ê key is released the
instruction in the program line just displayed is executed and the display then
shows the result of executing that line.
For example, to execute the program stored in the calculator one line at a time:
Keystrokes Display
gi.000
000,
Program line 000
Keystrokes
(RPN mode)
Display
fs
124.25
Sets calculator to Run mode and
to line 000 in program memory.
(Display shown assumes results
remain from previous
calculation.)
625
625.
Keys in price of typewriter.
Ê
001, 36
Program line 001: \
625.00
Result of executing program line
001.
Ê
002, 2
Program line 002: 2.
2.
Result of executing program line
002.
Ê
003, 5
Program line 003: 5.
25.
Result of executing program line
003.
Ê
004, 25
Program line 004: b
Section 8: Programming Basics 95
Pressing while the calculator is in Run mode sets the calculator to the
previous line in program memory, then displays that line’s number and the
keycode of the instruction stored there, just as in Program mode. In Run mode,
however, when the Ü key is released the display again shows the same
number as it did before was pressed: no instruction in program memory
is executed.
Interrupting Program Execution
Occasionally you’ll want a program to stop executing so that you can see an
intermediate result or enter new data. The HP 12C Platinum provides two
functions for doing so: u (pause) and t (run/stop).
Pausing During Program Execution
When a running program executes a u instruction, program execution halts
for about 1 second, then resumes. During the pause, the calculator displays the
last result calculated before the u instruction was executed.
If you press any key during a pause, program execution is halted indefinitely. To
resume program execution at the program line following that containing the u
instruction, press t.
Example: Create a program that calculates the entries in the AMOUNT, TAX,
and TOTAL columns for each item on the jewelry distributors invoice shown on
the next page, and also calculates the total in each of these columns for all items
on the invoice. Assume the sales tax is 6¾%.
To conserve lines of program memory, instead of keying in the tax rate before
the b instruction we’ll store it in register R
0
and recall it before the b
instruction. Before storing the program in program memory, we’ll calculate the
156.25
Result of executing program line
004.
Ê
005, 30
Program line 005: -
468.75
Result of executing program line
005.
Ê
006, 5
Program line 006: 5
5.
Result of executing program line
006.
Ê
007, 40
Program line 007: +
473.75
Result of executing program line
007 (the last line of the program).
Keystrokes
(RPN mode)
Display
96 Section 8: Programming Basics
required amounts for the first item on the invoice manually. The keystroke
sequence will use storage register arithmetic (described on page 25) in registers
R
1
, R
2
, and R
3
to calculate the column sums. Since these registers are cleared
when fCLEAR² is pressed, we’ll press those keys before beginning the
manual calculation – and also later, before running the program – to ensure that
the column sums are “initialized” to zero. (Pressing fCLEARH would clear
registers R
1
through R
3
, but would also clear R
0
, which will contain the tax rate.)
Pressing the gu keys is not necessary when we do the calculations
manually, since in Run mode the result of every intermediate calculation is
displayed automatically; but we’ll include u instructions in the program so
that the intermediate results AMOUNT and TAX are automatically displayed
when the program is executed.
Section 8: Programming Basics 97
Now, we’ll store the program in program memory. Do not key in the quantity and
cost of each item; these numbers will vary each time the program is run.
Keystrokes
(RPN mode)
Display
6.75?0
6.75
Stores tax rate in R
0
.
fCLEAR²
0.00
Clears the registers in R
1
through
R
6
.
13
13.
Keys in quantity of item.
\
13.00
Separates quantity of item from
cost of item to be keyed in next.
68.5
68.5
Keys in cost of item.
§
890.50
AMOUNT.
?+1
890.50
Adds AMOUNT to sum of
AMOUNT entries in register R
1
.
:0
6.75
Recalls tax rate to display.
b
60.11
TAX.
?+2
60.11
Adds TAX to sum of TAX entries
in register R
2
.
+
950.61
TOTAL.
?+3
950.61
Adds TOTAL to sum of TOTAL
entries in register R
3
.
Keystrokes
(RPN mode)
Display
fs
000,
Sets calculator to Program mode.
f]
000,
Sets RPN mode.
fCLEARÎ
000,
Clears program memory.
§
001, 20
gu
002, 43 31
Pauses to display AMOUNT.
?+1
003,44 40 1
:0
004,45 0
b
005, 25
gu
006, 43 31
Pauses to display TAX.
?+2
007,44 40 2
+
008, 40
?+3
009,44 40 3
98 Section 8: Programming Basics
Now, to run the program:
If the duration of the pause is not long enough to write down the number
displayed, you can prolong it by using more than one u instruction.
Alternatively, you can have the program automatically stop as described next.
Stopping Program Execution
Stopping Program Execution Automatically. Program execution is
automatically halted when the program executes a t instruction. To resume
executing the program from the program line at which execution was halted,
press t.
Keystrokes
(RPN mode)
Display
fs
950.61
Sets calculator to Run mode.
fCLEAR²
0.00
Clears registers R
1
– R
6
.
6.75?0 Stores tax rate.
13\68.5
68.5
Enters quantity and price of first
item on invoice.
t
890.50
AMOUNT for first item.
60.11
TAX for first item.
950.61
TOTAL for first item.
18\72.9
72.9
Enters quantity and price of
second item on invoice.
t
1,312.20
AMOUNT for second item.
88.57
TAX for second item.
1,400.77
TOTAL for second item.
24\85
85.
Enters quantity and price of third
item on invoice.
t
2,040.00
AMOUNT for third item.
137.70
TAX for third item.
2,177.70
TOTAL for third item.
5\345
345.
Enters quantity and price of
fourth item on invoice.
t
1,725.00
AMOUNT for fourth item.
116.44
TAX for fourth item.
1,841.44
TOTAL for fourth item.
:1
5,967.70
Sum of AMOUNT column.
:2
402.82
Sum of TAX column.
:3
6,370.52
Sum of TOTAL column.
Section 8: Programming Basics 99
Example: Replace the program above by one containing t instructions
instead of u instructions.
Keystrokes
(RPN mode)
Display
fs
000,
Sets calculator to Program mode.
f]
000,
Sets RPN mode.
fCLEARÎ
000,
Clears program memory.
§
001, 20
t
002, 31
Stops program execution to
display AMOUNT.
?+1
003,44 40 1
:0
004, 45 0
b
005, 25
t
006, 31
Stops program execution to
display TAX.
?+2
007,44 40 2
+
008, 40
?+3
009,44 40 3
fs
6,370.52
Sets calculator to Run mode.
fCLEAR²
0.00
Clears registers R
1
through R
6
.
13\68.5
68.5
First item.
t
890.50
AMOUNT for first item.
t
60.11
TAX for first item.
t
950.61
TOTAL for first item.
18\72.9
72.9
Second item.
t
1,312.20
AMOUNT for second item.
t
88.57
TAX for second item.
t
1,400.77
TOTAL for second item.
24\85
85.
Third item.
t
2,040.00
AMOUNT for third item.
t
137.70
TAX for third item.
t
2,177.70
TOTAL for third item.
5\345
345.
Fourth item.
t
1,725.00
AMOUNT for fourth item.
t
116.44
TAX for fourth item.
t
1,841.44
TOTAL for fourth item.
:1
5,967.70
Sum of AMOUNT column.
100 Section 8: Programming Basics
Program execution is also automatically halted when the calculator overflows
(refer to page page 73) or attempts an improper operation that results in an Error
display. Either of these conditions signifies that the program itself probably
contains an error.
To determine at which program line execution has halted (in order to locate the
error), press any key to clear the Error display, then press fs to set the
calculator to Program mode and display that program line.
You may also want to display the current program line (by pressing fs) if
your program has halted at one of several t instructions in your program and
you want to determine which one that is. To continue executing the program
afterward:
1. Press fs to set the calculator back to Run mode.
2. If you want to resume execution from the program line at which execution
halted rather than from line 000, press gi followed by three digit
keys that specify the program line desired.
3. Press t to resume execution.
Stopping Program Execution Manually. Pressing any key while a program is
running halts program execution. You may want to do this if the calculated
results displayed by a running program appear to be incorrect (indicating that the
program itself is incorrect).
To halt program execution during a pause in a running program (that is, when
u is executed), press any key.
After stopping program execution manually, you can determine at which
program line execution has halted and/or resume program execution as described
above.
:2
402.82
Sum of TAX column.
:3
6,370.52
Sum of TOTAL column.
Keystrokes
(RPN mode)
Display
101
Section 9
Branching and Looping
Although the instructions in a program normally are executed in order of their
program line numbers, in some situations it is desirable to have program
execution transfer or “branch” to a program line that is not the next line in
program memory. Branching also makes it possible to automatically execute
portions of a program more than once – a process called “looping.”
Simple Branching
The i (go to) instruction is used in a program to transfer execution to any
program line. The program line desired is specified by keying its three-digit line
number into the program line containing the i instruction. When the i
instruction is executed, program execution branches or “goes to” the program
line specified and then continues sequentially as usual.
You have already seen a common use of branching: the i000 instruction (that
is stored in program memory after the program you key in) transfers execution to
program line 000. A i instruction can be used to branch not only backward in
program memory – as in the case of i000 and as illustrated above – but also
forward in program memory. Backward branching is typically done to create
loops (as described next); forward branching is typically done in conjunction
with an o or m instruction for conditional branching (as described
afterward).
Looping
If a i instruction specifies a lower-numbered line in program memory, the
instructions in the program lines between the specified line and the i
instruction will be executed repeatedly. As can be seen in the illustration above
under Simple Branching, once the program begins executing the “loop” it will
execute it again and again.
102 Section 9: Branching and Looping
If you want to terminate the execution of a loop, you can include an o or m
instruction (described below) or an t instruction within the loop. You can
also terminate execution by pressing any key while the loop is being executed.
Example: The following program automatically amortizes the payments on a
home mortgage without requiring you to press f! for each payment. It will
amortize one month’s payments each time or one years payments each time the
loop is executed, depending on whether the number 1 or 12 is in the display
when you start running the program. Before running the program, we’ll
“initialize” it by storing the required data in the financial registers – just as we
would do if we were amortizing a single payment manually. We’ll run the
program for a $50,000 mortgage at 12¾% for 30 years, and we’ll key 1 into the
display just before running it in order to amortize monthly payments. For the
first two “passes” through the loop we’ll execute the program one line at a time,
using Ê, so that we can see the looping occurring; then we’ll use t to
execute the entire loop a third time before terminating execution.
Keystrokes Display
fs
000,
Sets calculator to Program mode.
f]
000,
Sets RPN mode.
fCLEARÎ
000,
Clears program memory.
?0
001, 44 0
Stores the number from the
display into register R
0
. This
number will be the number of
payments to be amortized.
:0
002, 45 0
Recalls the number of payments
to be amortized. This program
line is the one to which program
execution will later branch. It is
included because after the first
time the loop is executed, the
number in the “display”
a
is
replaced by the result of !.
f!
003, 42 11
Amortizes payment(s).
gu
004, 43 31
Pauses to display amount of
payment(s) applied to interest.
~
005, 34
Brings amount of payment(s)
applied to principal into
“display.”
a
gu
006, 43 31
Pauses to display amount of
payment(s) applied to principal.
Section 9: Branching and Looping 103
gi002
007,43,33,002
Transfers program execution to
line 002, so that the number of
payments to be amortized can be
recalled to the display before the
! instruction in line 003 is
executed.
fs
0.00
Sets calculator to Run mode.
(Display shown assumes no
results remain from previous
calculations.)
fCLEARG
0.00
Clears financial registers.
30gA
360.00
Enters n.
12.75gC
1.06
Enters i.
50000$
50,000.00
Enters PV.
50,000.00
Sets payment to End.
P
–543.35
Calculates the monthly payment.
0n
0.00
Reset n to zero.
1
1.
Keys 1 into the display to
amortize monthly payments.
Ê
001, 44 0
Line 001: ?0.
1.00
Ê
002, 45 0
Line 002: :0. This is the
beginning of the first pass through
the loop.
1.00
Ê
003, 42 11
Line 003: f!.
–531.25
Portion of first month’s payment
applied to interest.
Ê
004, 43 31
Line 004: gu.
–531.25
Ê
005, 34
Line 005: ~.
–12.10
Portion of first month’s payment
applied to principal.
Ê
006, 43 31
Line 006: gu.
–12.10
Ê
007,43,33,002
Line 007: gi002. This is the
end of the first pass through the
loop.
–12.10
Keystrokes Display
104 Section 9: Branching and Looping
Conditional Branching
Often there are situations when it is desirable for a program to be able to branch
to different lines in program memory, depending on certain conditions. For
example, a program used by an accountant to calculate taxes might need to
branch to different program lines depending on the tax rate for the particular
income level.
Ê
002, 45 0
Line 002: :0. Program
execution has branched to the
beginning of the loop for the
second pass through it.
1.00
Ê
003, 42 11
Line 003: f!.
–531.12
Portion of second month’s
payment applied to interest.
Ê
004, 43 31
Line 004: gu.
–531.12
Ê
005, 34
Line 005: ~.
–12.23
Portion of second month’s
payment applied to principal.
Ê
006, 43 31
Line 006: gu.
–12.23
Ê
007,43,33,002
Line 007: gi002.
This is the end of the second pass
through the loop.
–12.23
t
–530.99
Portion of third month’s payment
applied to interest.
–12.36
Portion of third month’s payment
applied to principal.
t(or any key)
–12.36
Halts program execution.
a More precisely, the number in the X-register.
Keystrokes Display
Section 9: Branching and Looping 105
The HP 12C Platinum provides two conditional test instructions that are used in
programs for conditional branching:
z o tests whether the number in the X-register (represented by the x in the
key symbol) is less than or equal to the number in the Y-register
(represented by the y in the key symbol). As discussed in Appendix A, the
number in the X-register is simply the number that would, if the calculator
were in Run mode, be currently in the display; and the number in the Y-
register is the number that would, if the calculator were in Run mode, have
been in the display when \ was pressed. For example, pressing 4\5
would place the number 4 in the Y-register and the number 5 in the
X-register.
z m tests whether the number in the X-register is equal to zero.
The possible results of executing either of these instructions are:
z If the condition tested for is true when the instruction is executed, program
execution continues sequentially with the instruction in the next line of
program memory.
z If the condition tested for is false when the instruction is executed,
program execution skips the instruction in the next line of program
memory and continues with the instruction in the following line.
These rules can be summarized as “DO if TRUE”.
The program line immediately following that containing the conditional test
instruction can contain any instruction; however, the most commonly used
instruction there is i. If a i instruction follows a conditional test
instruction, program execution branches elsewhere in program memory if the
condition is true and continues with the next line in program memory if the
condition is false.
106 Section 9: Branching and Looping
Example: The following program calculates income tax at a rate of 20% on
incomes of $20,000 or less and 25% on incomes of more than $20,000. To
conserve program lines, the program assumes that the test value – 20,000 – has
been stored in register R
0
and the tax rates – 20 and 25 – have been stored in
registers R
1
and R
2
, respectively.
Note: If a program requires that certain numbers be in the X- and
Y-registers when instructions such as o are executed, it is extremely
helpful when writing the program to show the quantities in each register
after each instruction is executed, as in the following diagram.
We’ll key the income into the display before running the program so that it will
be in the X-register when the :0 instruction in program line 001 is executed.,
This instruction will place the test value 20,000 in the X-register and (as
explained in Appendix A) move the income into the Y-register. The ~
instruction in program line 002 will exchange the numbers in the X- and
Section 9: Branching and Looping 107
Y-registers (as also explained in Appendix A): that is, it will place the income
back into the X-register and place the test value into the Y-register. This is
necessary because when either the :2 instruction in line 005 or the :1
instruction in line 007 is executed, the number in the X-register is moved into the
Y-register; if the ~ instruction were not included, the test value 20,000, rather
than the income, would be in the Y-register when the b instruction in line 008
is executed.
Now, we'll store the required numbers in registers R
0
, R
1
, and R
2
, then we’ll run
the program, using Ê so that we can check that the branching occurs properly.
It’s good practice with programs containing conditional test instructions to check
that the program branches correctly for all possible conditions: in this case, if the
income is less than, equal to, or greater than the test value.
Keystrokes
(RPN mode)
Display
fs
007,43,33,002
Sets calculator to Program mode.
(Display shows program line at
which execution was halted at end
of preceding example.)
f]
007,43,33,002
Sets RPN mode.
fCLEARÎ
000,
Clears program memory.
:0
001, 45 0
Recalls test value into X register
and places income in Y-register.
~
002, 34
Places income in X register and
test value in Y-register.
go
003, 43 34
Tests whether number in
X-register (income) is less than or
equal to number in Y-register
(20,000).
gi007
004,43,33,007
If condition is true, branches to
program line 007.
:2
005, 45 2
If condition is false, recalls 25%
tax rate to X-register.
gi008
006,43,33,008
Branches to program line 008.
:1
007, 45 1
Recalls 20% tax rate to X-register.
b
008, 25
Calculates tax.
fs
–12.36
Sets calculator to Run mode.
(Display shows results of running
of previous program.)
108 Section 9: Branching and Looping
Keystrokes
(RPN mode)
Display
20000?0
20,000.00
Stores test value in register R
0
.
20?1
20.00
Stores 20% tax rate in register R
1
.
25?2
25.00
Stores 25% tax rate in register R
2
.
15000
15,000.
Keys income less than test value
into display and X-register.
Ê
001, 45 0
Line 001: :0.
20,000.00
Test value has been recalled to
X-register, moving income to
Y-register.
Ê
002, 34
Line 002: ~
15,000.00
Income has been placed in
X-register and test value has been
placed in Y-register.
Ê
003, 43 34
Line 003: go
15,000.00
Ê
004,43,33,007
Condition tested by o was
true, so program execution
continued with line 004:
gi007.
15,000.00
Ê
007, 45 1
Line 007: :1.
20.00
20% tax rate has been recalled to
X-register, moving income to Y-
register.
Ê
008, 25
Line 008: b.
3,000.00
20% of 15,000 = 3,000.
20000
20,000.
Keys income equal to test value
into display and X-register.
Ê
001, 45 0
Line 001: :0.
20,000.00
Test value has been recalled to X-
register, moving income to Y-
register.
Ê
002, 34
Line 002: ~.
20,000.00
Income has been placed in X-
register and test value has been
placed in Y-register.
Section 9: Branching and Looping 109
Ê
003, 43 34
Line 003 go.
20,000.00
Ê
004,43,33,007
Condition tested by o was
true, so program execution
continued with line 004:
gi007.
20,000.00
Ê
007, 45 1
Line 007: :1.
20.00
20% tax rate has been recalled to
X-register, moving income to Y-
register.
Ê
008, 25
Line 008: b.
4,000.00
20% of 20,000 = 4,000.
25000
25,000.
Keys income greater than test
value into display and X-register
Ê
001, 45 0
Line 001: :0.
20,000.00
Test value has been recalled to X-
register, moving income to Y-
register.
Ê
002, 34
Line 002: ~.
25,000.00
Income has been placed in X-
register and test value has been
placed in Y-register.
Ê
003, 43 34
Line 003: go.
25,000.00
Ê
005, 45 2
Condition tested by o was
false, so program execution
skipped the next line and
continued at line 005: :2.
25.00
25% tax rate has been recalled to
X-register, moving income to Y-
register.
Ê
006,43,33,008
Line 006: gi008.
25.00
Ê
008, 25
Line 008: b.
6,250.00
25% of 25,000 = 6,250.
Keystrokes
(RPN mode)
Display
110
Section 10
Program Editing
There are various reasons why you might want to modify a program you have
stored in Program memory: to correct a program that turns out to have errors; to
insert new instructions such as ? to store intermediate results or u to
display intermediate results; or to replace a u instruction by an t
instruction.
Rather than clearing program memory and keying in the modified program, you
can modify the program already stored in the calculator. This is called program
editing.
Changing the Instruction in a Program Line
To change a single instruction in program memory:
1. Press fs to set the calculator to Program mode.
2. Use Ê, Ü, or i. to set the calculator to the program line
preceding the line containing the instruction to be changed.
3. Key in the new instruction.
For example, to change the instruction stored in program line 005, press
gi.004, then key in the new instruction that is to be stored in program
line 005. The instruction previously stored in line 005 will be replaced; it is not
automatically “bumped” into line 006.
Example: With the last program from the preceding section still stored in the
calculator, suppose you wanted to use register R
2
for some other purpose, and so
you needed to replace the :2 instruction in program line 005 with, say, :6.
You could change the instruction in line 005 as follows:
Keystrokes Display
fs
000,
Sets calculator to Program mode.
f]
000,
Sets RPN mode.
gi.004
004,43,33,007
Sets calculator to program line
preceding that containing the
instruction to be changed.
:6
005, 45 6
Keys new instruction into
program line 005, replacing the
:2 instruction previously
there.
Section 10: Program Editing 111
Adding Instructions at the End of a Program
To add one or more instructions at the end of the last program stored in program
memory:
1. Press fs to set the calculator to Program mode.
2. Press gi. followed by three digits that specify the last line you
keyed into program memory (that is, the highest numbered line, not
necessarily the line most recently keyed in).
3. Key in the new instruction or instructions.
Note: To add one or more instructions at the end of a program that is not
the last program stored in program memory, use the procedure described
below under Adding Instructions Within a Program.
Example: With the last program from the preceding section stored in the
calculator, suppose you wanted to add a - instruction at the end in order to
calculate the net income after taxes. You could do so as follows:
Ê
006,43,33,008
Shows that instruction in program
line 006 has not been changed.
fs
6,250.00
Sets calculator back to Run mode.
(Display shown assumes results
remain from last example in
preceding section.)
:2?6
25.00
Copies tax rate from R
2
into R
6
.
Keystrokes
(RPN mode)
Display
fs
000,
Sets calculator to Program mode.
f]
000,
Sets RPN mode.
gi.008
008, 25
Sets calculator to last line keyed
into program memory.
-
009, 30
Keys new instruction into
program line 009.
fs
25.00
Sets calculator back to Run mode.
15000t
12,000.00
Net income after 20% tax is
subtracted from $15,000 income.
Keystrokes Display
112 Section 10: Program Editing
Adding Instructions Within a Program
If an instruction is to be added within a program, simply keying it in will replace
the instruction previously stored in that program line, as described above; the
contents of all higher-numbered program lines remain unchanged.
To add instructions within a program, you could simply key in the new
instructions, beginning at the proper program line, followed by the original
instructions from that program line through the end of the program. This method
is described below under Adding Instructions by Replacement. When
instructions must be added in the middle of a long program, however, using this
method will require you to key in numerous instructions – namely, the original
instructions from the point at which the new instructions are added through the
end of program memory. Since keying in these instructions may require a
significant amount of time, in such situations you may prefer to use the method
described below under Adding Instructions by Branching.
That method basically involves branching to the new instructions which are
stored at the end of program memory, then branching back to the program line
immediately following the line from which you branched out. Adding instruc-
tions by branching is not so simple as adding instructions by replacement; how-
ever, it generally will require fewer keystrokes whenever there are more than
four program lines between (and including) the first line to be executed after the
new instruction(s) and the last line you keyed into program memory. Further-
more, if program memory includes branches to program lines following the point
at which the new instruction(s) are being added, adding instructions by branch-
ing will not require that you change the line numbers specified in the i
instructions, which may be necessary when you add instructions by replacement.
Adding Instructions by Replacement
1. Press fs to set the calculator to Program mode.
2. Press gi. followed by three digits that specify the last program line
to be executed before the added instruction(s). This sets the calculator to
the proper program line for adding the new instruction(s) in the next step.
3. Key in the new instruction or instructions.
4. Key in the original instruction or instructions, beginning with the first
instruction to be executed after the added instruction(s), and continuing
through the last instruction you keyed into program memory.
Note: If program memory includes branches to program lines following
that at which the first new instruction is being added, remember to change
the line number(s) specified in the i instruction(s) – as described above
under Changing the Instruction in a Program Line – to the actual new line
number(s).
Section 10: Program Editing 113
Example: Assuming you have added a - instruction at the end of program
memory as in the preceding example, suppose you now wanted to insert an t
instruction before the - instruction so that the program will display the amount
of the tax before displaying the net income after tax. Since there is only one
instruction (-) following the point at which the new instruction is being added,
it is simplest to add the t instruction by replacement, as follows:
Adding Instructions by Branching
1. Press fs to set the calculator to Program mode.
2. Press gi. followed by three digits that specify the program line
immediately preceding the point at which the new instruction(s) are being
added – usually, the last program line to be executed before the added
instruction(s). This sets the calculator to the proper program line for
inserting a i instruction in the next step. This i instruction will
replace whatever instruction was already stored there, but that instruction
will be keyed back into program memory, to be executed just after the new
instructions, in step 7.
3. Press gi followed by three digits that specify the second line after the
last line you keyed into program memory. (Branching to the second line
rather than to the first is necessary because the first line following the last
program in program memory must contain a i000 instruction. The
i000 instruction ensures that program execution will branch to line
000 and halt after the program is run.) For example, if the last line you
keyed into program memory was line 010, you would press gi012 at
this step, preserving the gi000 in line 011.
Keystrokes
(RPN mode)
Display
fs
000,
Sets calculator to Program mode.
f]
000,
Sets RPN mode.
gi.008
008, 25
Sets calculator to last program
line to be executed, which
contains the b instruction.
t
009, 31
Keys in new instruction.
-
010, 30
Keys in original instruction,
which was replaced by new
instruction added.
fs
12,000.00
Sets calculator back to Run mode.
15000t
3,000.00
Twenty percent tax on $15,000
income.
t
12,000.00
Net income after tax.
114 Section 10: Program Editing
4. Press gi. followed by three digits that specify the last line you
keyed into program memory.
5. Press gi000. This automatically converts a data storage register into
seven additional lines of program memory (if there was not already a
i000 instruction remaining at the end of program memory), and it
ensures that program execution will branch to line 000 after the program is
run.
6. Key in the instruction(s) being added.
7. Key in the instruction that originally immediately followed the point at
which the new instruction(s) are being added – that is, the first instruction
to be executed after the added instruction(s). (This instruction was
replaced by the i instruction keyed in at step 3.)
8. Press gi followed by three digits that specify the second line
following the point at which the new instruction(s) are being added. This
i instruction will cause program execution to branch back to the proper
line within the original program.
Example: Continuing with the preceding example, suppose incomes less than or
equal to $7,500 were not to be taxed. You could modify the program to check for
this condition and stop at line 000, displaying the original income keyed in, by
storing 7,500 in register R
3
and adding the following instructions between lines
000 and 001: :3~gogi000. Since there are more than four
instructions between (and including) the first line to be executed after the added
instructions (line 001) and the last line you keyed into program memory (line
010), it will require fewer keystrokes to add the new instructions by branching
than to add them by replacement.
Keystrokes
(RPN mode)
Display
fs
000,
Sets calculator to Program mode.
f]
000,
Sets RPN mode.
gi.000
000,
Sets calculator to program line
immediately preceding point at
which new instructions are being
added. (In this particular example,
this step could have been skipped
since calculator was already set at
the proper program line.)
gi012
001,43,33,012
Branches to program line 012, the
second line after last line of
program.
Section 10: Program Editing 115
The following illustration of the edited program shows how program execution
branches to the instructions added at the end of program memory, then branches
back.
gi.010
010, 30
Sets calculator to last line of
program so that i000
instruction keyed in next will be
stored in first line following
program.
gi000
011,43,33,000
Ensures that i000 instruction
follows program.
:3
012, 45 3
Added instructions.
~
013, 34
go
014, 43 34
gi000
015,43,33,000
:0
016, 45 0
Keys in instruction immediately
following point at which new
instructions are being added. (This
instruction was replaced in line 001
by i012 instruction.)
gi002
017,43,33,002
Branches back to second line (line
002) following point at which new
instructions are being added.
fs
12,000.00
Sets calculator back to Run mode.
7500?3
7,500.00
Stores test value in register R
3
.
6500t
6,500.00
Runs program for income less than
$7,500. Display shows original
income keyed in, indicating that tax
is zero.
15000t
3,000.00
Tax on $15,000 income.
t
12,000.00
Net income after tax. This shows
program still works for an income
greater than $7,500 and less than
$20,000.
Keystrokes
(RPN mode)
Display
116 Section 10: Program Editing
117
Section 11
Multiple Programs
You can store multiple programs in program memory, provided that you separate
them by instructions that will halt program execution after each program is run
and return to the beginning of the program if it is run again. You can run
programs after the first one stored in program memory by setting the calculator
to the first line of the program using i before pressing t.
Storing Another Program
To store a program after another program is already stored in program memory:
1. Press fs to set the calculator to Program mode. Do not clear program
memory.
2. Press gi. followed by three digits that specify the number of the
last line you keyed into program memory.
Note: If this is the second program to be stored in program memory, you
will need to ensure that a i000 instruction separates it from the first
program by doing step 3. If there are already two or more programs stored
in program memory, skip step 3 and proceed with step 4.
3. Press gi000. This automatically converts a data storage register into
seven additional lines of program memory (if there was not already a
i000 instruction remaining at the end of program memory), and it
ensures that program execution will branch to line 000 after the first
program is run.
4. Key the program into program memory. If you are storing a program that
you originally had written to be stored at the beginning of program
memory and the program contains a i instruction, be sure to change the
line number specified in the instruction so that the program will branch to
the actual new line number.
Note: The next two steps are included so that program execution will halt
after this program is run and will return to the beginning of the program if
it is run again. If the program ends with a loop, you should skip steps 5 and
6 since the instructions in those steps would serve no purpose and never be
executed.
5. Press t. This halts program execution at the end of the program.
6. Press gi followed by three digit keys that specify the first line
number of your new program. This transfers program execution to the
beginning of the new program when the program is run again.
118 Section 11: Multiple Programs
Example 1: Assuming that program memory still contains the last program from
the preceding section (which consisted of 17 program lines), store after that
program the office-supplies program from Section 8 (page 86). Since this is the
second program to be stored in program memory, we’ll ensure that a i000
instruction separates it from the first program by doing step 3 in the procedure
above. Furthermore, since this program does not end with a loop, we’ll do steps
5 and 6 too.
Example 2: With the two programs now stored in program memory from the
preceding examples (occupying 27 program lines), store the amortization
program from Section 9 (page 102). Since there are already two programs stored
in program memory, we’ll skip step 3 in the procedure above. Furthermore, since
the amortization program ends with a loop, we’ll skip steps 5 and 6. When the
amortization program was stored at the beginning of program memory, the i
instruction at the end of the program branched to the :0 instruction in line
002. Since the :0 instruction is now in line 029, we’ll specify that line
number with the i instruction in line 034.
Keystrokes
(RPN mode)
Display
fs
000,
Sets calculator to Program mode.
f]
000,
Sets RPN mode.
gi.017
017,43,33,002
Sets calculator to last line keyed
into program memory.
gi000
018,43,33,000
Ensures that second program is
separated from first by i000.
\
019, 36
Keys in program.
2
020, 2
5
021, 5
b
022, 25
-
023, 30
5
024, 5
+
025, 40
t
026, 31
Halts program execution.
gi019
027,43,33,019
Branches to beginning of program.
fs
12,000.00
Sets calculator back to Run mode.
(Display shown assumes results
remain from running program in
previous example.)
Section 11: Multiple Programs 119
Running Another Program
To run a program that does not begin with program line 001:
1. Press fs to set the calculator to Run mode. If the calculator is already
in Run mode, skip this step.
2. Press gi followed by three digits that specify the first line of the
program.
3. Press t.
Example: Run the office-supplies program, now stored in the calculator
beginning at program line 019, for the typewriter listing for $625.
Keystrokes Display
fs
000,
Sets calculator to Program mode.
f]
000,
Sets RPN mode.
gi.027
027,43,33,019
Sets calculator to last line keyed
into program memory.
?0
028, 44 0
Keys in program
:0
029, 45 0
f!
030, 42 11
gu
031, 43 31
~
032, 34
gu
033, 43 31
gi029
034,43,33,029
Keystrokes Display
fs
12,000.00
Sets calculator to Program
mode.
f]
12,000.00
Sets RPN mode.
gi019
12,000.00
Sets calculator to first line of
program to be executed.
625t
473.75
Net cost of typewriter.
Part III
Solutions
122
Section 12
Real Estate and Lending
Annual Percentage Rate Calculations With Fees
Borrowers are usually charged fees in connection with the issuance of a
mortgage, which effectively raises the interest rate. The actual amount received
by the borrower (PV) is reduced, while the periodic payments remain the same.
Given the life or term of the mortgage, the interest rate, the mortgage amount,
and the basis of the fee charge (how the fee is calculated), the true Annual
Percentage Rate (APR) may be calculated. Information is entered as follows:
1. Press and fCLEARG.
2. Calculate and enter the periodic payment amount of the loan.
a. Key in the total number of payment periods; press n.
b. Key in the periodic interest rate (as a percentage); press ¼.
c. Key in the mortgage amount; press $.
1
d. To obtain the periodic payment amount, press P.
1
3. Calculate and key in the actual net amount disbursed.
1
z If fees are stated as a percentage of the mortgage amount (points), recall
the mortgage amount (:$) key in the fee (percentage) rate; press
b-$.
z If fees are stated as a flat charge, recall the mortgage amount
(:$); key in the fee amount (flat charge); press -$.
z If fees are stated as a percentage of the mortgage amount plus a flat
charge, recall the mortgage amount (:$); key in the fee
(percentage) rate, press b-; key in the fee amount (flat charge);
press -$.
4. Press ¼ to obtain the interest rate per compounding period.
5. To obtain the annual nominal percentage rate, key in the number of periods
per year, then press §.
1.
Positive for cash received; negative for cash paid out.
Section 12: Real Estate and Lending 123
Example 1: A borrower is charged 2 points for the issuance of his mortgage. If
the mortgage amount is $60,000 for 30 years and the interest rate is 11½% per
year, with monthly payments, what true annual percentage rate is the borrower
paying? (One point is equal to 1% of the mortgage amount.)
Example 2: Using the same information as given in example 1, calculate the
APR if the mortgage fee is $150 instead of a percentage.
Keystrokes (RPN mode) Display
fCLEARG
30gA
360.00
Months (into n)
11.5gC
0.96
Percent monthly interest rate (into
i).
60000$
60,000.00
Loan amount (into PV).
P
–594.17
Monthly payment (calculated).
:$2b-$
58,800.00
Actual amount received by
borrower (into PV).
¼
0.98
Percent monthly interest rate
(calculated).
12§
11.76
Annual percentage rate.
Keystrokes (RPN mode) Display
fCLEARG
30gA
360.00
Months (into n)
11.5gC
0.96
Percent monthly interest rate (into
i).
60000$
60,000.00
Loan amount (into PV).
P
–594.17
Monthly payment (calculated).
:$150-$
59,850.00
Effective mortgage amount (into
PV).
¼
0.96
Monthly interest rate (calculated).
12§
11.53
Annual percentage rate.
124 Section 12: Real Estate and Lending
Example 3: Again using the information given in example 1, what is the APR if
the mortgage fee is stated as 2 points plus $150?
Price of a Mortgage Traded at a Discount or
Premium
Mortgages may be bought and/or sold at prices lower (discounted) or higher (at a
premium) than the remaining balance of the loan at the time of purchase. Given
the amount of the mortgage, the periodic payment, the timing and amount of the
balloon or prepayment, and the desired yield rate, the price of the mortgage may
be found. It should be noted that the balloon payment amount (if it exists) occurs
coincident with, and does not include, the last periodic payment amount.
Information is entered as follows:
1. Press and fCLEARG.
2. Key in the total number of periods until the balloon payment or
prepayment occurs; press n. (If there is no balloon payment, key in total
number of payments and press n.)
3. Key in the desired periodic interest rate (yield) and press ¼.
4. Key in the periodic payment amount; press P.
2
5. Key in the balloon payment amount and press M.
2
(If there is no balloon
payment, go to step 6.)
6. Press $ to obtain the purchase price of the mortgage.
Keystrokes (RPN mode) Display
fCLEARG
30gA
360.00
Months (into n)
11.5gC
0.96
Percent monthly interest rate (into
i).
60000$
60,000.00
Loan amount (into PV).
P
–594.17
Monthly payment (calculated).
:$2b-
58,800.00
150-$
58,650.00
Effective mortgage amount (into
PV).
¼
0.98
Monthly interest rate (calculated).
12§
11.80
Annual percentage rate.
2.
Positive for cash received; negative for cash paid out.
Section 12: Real Estate and Lending 125
Example 1: A lender wishes to induce the borrower to prepay a low interest rate
loan. The interest rate is 5% with 72 payments remaining of $137.17 and a
balloon payment at the end of the sixth year of $2000. If the lender is willing to
discount the future payments at 9%, how much would the borrower need to
prepay the note?
Example 2: A 9½% mortgage with 26 years remaining and a remaining balance
of $49,350 is available for purchase. Determine the price to pay for this
mortgage if the desired yield is 12%. (Since the payment amount is not given, it
must be calculated.)
Yield of a Mortgage Traded at a Discount or
Premium
The annual yield of a mortgage bought at a discount or premium can be
calculated given the original mortgage amount, interest rate, and periodic
Keystrokes (RPN mode) Display
fCLEARG
72n
72.00
Months (into n).
9gC
0.75
Discount rate (into i).
137.17P
a
a Note that the payments are positive because this problem in seen from the viewpoint of
the lender who will be receiving payments. The negative PV indicates money that was
lent out.
137.17
Monthly payments (into PMT).
2000M$
–8,777.61
Amount necessary to prepay the
note.
Keystrokes Display
fCLEARG
26gA
312.00
Months (into n).
9.5gC
0.79
Percent monthly interest rate (into
i).
49350Þ$P
427.17
Monthly payment to be received
(calculated).
12gC
1.00
Desired monthly interest rate (into
i).
$
–40,801.57
Purchase price to achieve the
desired yield (calculated).
126 Section 12: Real Estate and Lending
payment, as well as the number of payment periods per year, the price paid for
the mortgage, and the balloon payment amount (if it exists).
Information is entered as follows:
1. Press and fCLEARG.
2. Key in the total number of periods until the balloon payment occurs and
press n. (If there is no balloon payment, key in the total number of
periods and press n.)
3. Key in the periodic payment amount then press P.
3
4. Key in the purchase price of the mortgage then press $.
3
5. Key in the balloon payment amount then press M.
3
(If there is no balloon
payment, go to step 6.)
6. Press ¼ to obtain the yield per period.
7. Key in the number of periods per year and press § to obtain the nominal
annual yield.
Example 1: An investor wishes to purchase a $100,000 mortgage taken out at
9% for 21 years. Since the mortgage was issued, 42 monthly payments have been
made. What would be the annual yield if the purchase price of the mortgage is
$79,000? (Since PMT was not given, it must be calculated).
3. Positive for cash received; negative for cash paid out.
Keystrokes (RPN mode) Display
fCLEARG
21gA
252.00
Enter the number of periods (into n).
9gC
0.75
Monthly interest rate (into i).
100000Þ$
–100,000.00
Mortgage amount (into PV; negative
to indicate money paid out).
P
884.58
Payment received (calculated).
:n
252.00
Recall number of periods.
42-n
210.00
Number of periods left after mortgage
is bought (into n).
79000Þ$
–79,000.00
Input price of mortgage (into PV;
negative to indicate money paid out).
¼
0.97
Yield per month (calculated).
12§
11.68
Percent annual yield.
Section 12: Real Estate and Lending 127
Example 2: Using the same information given in example 1, calculate the
annual yield if the loan is to be paid in full at the end of the fifth year (from
original issuance). (In this case both the payment amount and the balloon must
be calculated since they are not given.)
Calculate the remaining balance of the loan after five years.
The Rent or Buy Decision
The question of whether to rent or purchase a residence is not always easy to
answer, especially when the time period over which you would own or rent a
house is short. This program (written in RPN mode) performs an analysis which
could be helpful in reaching a decision. Essentially, it calculates a yield or rate of
return on the proposed investment. This yield may be compared with the yield
obtained by renting a residence and investing the down payment and monthly
payment differences in a savings account or other investment opportunity. This
program takes into account the tax advantages obtained by a home owner on
property taxes and mortgage interest.
First the program computes the Net Cash Proceeds upon Resale (NCPR),
4
next
the yield on the investment in the house and then the value of the hypothetical
savings account at the end of the investment period. A comparison of the NCPR
and the final balance of the savings account and a comparison of the yields
should aid in determining whether to rent or buy.
Keystrokes (RPN mode) Display
fCLEARG
21gA
252.00
Input the number of periods (into n).
9gC
0.75
Monthly interest rate (into PV).
100000Þ$
–100,000.00
Mortgage amount (into PV).
P
884.58
Payment (calculated).
5gA
60
Number of periods to be amortized.
M
89,849.34
Remaining balance of the loan after
five years.
:n
60.00
42-n
18.00
New life of loan.
79000Þ$¼
1.77
Percent monthly yield. (calculated).
12§
21.29
Percent annual yield.
4.
The Net Cash Proceeds upon Resale (NCPR = sales price – commission – mortgage
balance), is the pre-tax proceeds. The program assumes that the buyer reinvests in like
property and is not subject to capital gains tax.
128 Section 12: Real Estate and Lending
KEYSTROKES
(RPN mode)
DISPLAY
KEYSTROKES
(RPN mode)
DISPLAY
fs Þ
032, 16
f] M
033, 15
fCLEAR
Î
000,
t
034, 31
M
001, 15
d
035, 33
M
a
002, 15
:n
036, 45 11
:7
003, 45 7
z
037, 10
b
004, 25
:4
038, 45 4
-
005, 30
-
039, 30
:n
006, 45 11
:.0
040, 45 48 0
?0
007, 44 0
b
041, 25
:$
008, 45 13
:P
042, 45 14
fCLEAR
G
009, 42 34
:4
043, 45 4
:1
010, 45 1
-
044, 30
-
011, 30
:5
045, 45 5
$
012, 13
-
046, 30
:3
013, 45 3
:8
047, 45 8
gC
014, 43 12
+
048, 40
:2
015, 45 2
-
049, 30
gA
016, 43 11
Þ
050, 16
P
017, 14
P
051, 14
d
018, 33
:0
052, 45 0
d
019, 33
gA
053, 43 11
0
020, 0
:1
054, 45 1
n
021, 11
:6
055, 45 6
:0
022, 45 0
+
056, 40
Section 12: Real Estate and Lending 129
1. Key in the program.
2. Key in the estimated down payment then press ?1.
3. Key in the life of the mortgage then press ?2.
4. Key in the annual mortgage interest rate then press ?3.
5. Key in the estimated monthly taxes then press ?4.
6. Key in the total amount estimated for monthly repairs, improvements,
incremental insurance, utility costs, and other expenses, then press ?5.
7. Key in the closing costs then press ?6.
8. Key in the selling cost as a percentage of the selling price. This should
include sales commission, escrow fees, etc. then press ?7.
1
023, 1
Þ
057, 16
2
024, 2
$
058, 13
§
025, 20
¼
059, 12
f!
026, 42 11
:gC
060, 45,43 12
d
027, 33
t
061, 31
d
028, 33
:9
062, 45 9
d
029, 33
gC
063, 43 12
:$
030, 45 13
M
064, 15
+
031, 40
fs
a FV is repeated in the program twice to ensure that it is computed and not stored.
REGISTERS
n: Period i: Apprec. PV: Price PMT: Used
FV: Used R
0
: Period R
1
: Dwn Pmt R
2
: Life
R
3
: i(Mtg) R
4
: Taxes/Mo R
5
: Improve. R
6
: Closing C.
R
7
: % Comm. R
8
: Rent R
9
: Savings i R
.0
: Bracket
R
.1
: Unused
KEYSTROKES
(RPN mode)
DISPLAY
KEYSTROKES
(RPN mode)
DISPLAY
130 Section 12: Real Estate and Lending
9. Key in the monthly rent for the alternative housing then press ?8.
10. Key in the savings or alternative investment annual interest rate as a
percentage then press ?9.
11. Key in the combined State and Federal marginal tax rate
5
as a percentage
then press ?.0.
12. Press fCLEARG then key in the number of years involved in the
investment; press n.
13. Key in the estimated rate of yearly appreciation as a percentage then press
¼.
14. Key in the price of the house under consideration then press $.
15. Press t to compute the net proceeds from the sale of the house. (A
negative value indicates money lost.)
16. Press t to compute the yield on your investment in the house.
6
17. Press t to compute the value of a savings account or other investment.
18. Compare the value of the hypothetical savings account to the net proceeds
of the sale of the house. Examine the sign and magnitude of the yield to
arrive at your decision.
19. To change data and repeat the calculations, store the changed values in the
appropriate registers and go to step 12.
Example: You are being transferred for 4 years to a distant city and are faced
with the decision of whether to rent or to buy a house. A quick survey of the
housing market indicates that you can purchase an acceptable house for $70,000
with a $7,000 down payment on a 30 year mortgage at 12% interest. The closing
costs would be about $1200. Selling costs include a 6% commission for resale
and miscellaneous other fees that amount to another 2% of the sale price.
Housing in the area is appreciating 10% per year. Property taxes would be about
$110 per month, and you estimate that maintenance would cost an additional $65
per month.
5.
The user should key in the total marginal income tax – Federal plus State – to obtain
calculations which reflect the tax advantages of home ownership. Because of the
complexities of tax laws and different financial and tax considerations for each individual,
this program should only serve as a guide in considering an investment of this type. For more
specific, detailed information, consult a tax accountant or qualified tax advisor.
6.
If the calculator displays a negative result or Error 5 when solving for yield then your
investment has resulted in a loss. The amount of interest earned on the alternative investment
is not taken into account in this calculation.
Section 12: Real Estate and Lending 131
An alternative would be to rent a similar dwelling at $400 per month and to
invest the difference between the purchase cost and rent at 6¼% interest. Your
personal income tax rate (marginal) is 25% Federal and 5% State. Which
alternative is more financially attractive?
By purchasing a house, you would gain $10,858.08 (32,391.87 – 21,533.79) over
an alternate investment at 6.25% interest.
Deferred Annuities
Sometimes transactions are established where payments do not begin for a
specified number of periods; the payments are deferred. The technique for
calculating NPV may be applied assuming zero for the first cash flow. Refer to
pages 59 through 63.
Example 1: You have just inherited $20,000 and wish to put some of it aside for
your daughters college education. You estimate that when she is of college age,
9 years from now, she will need $7,000 at the beginning of each year for 4 years
for college tuition and expenses. You wish to establish a fund which earns 6%
annually. How much do you need to deposit in the fund today to meet your
daughters educational expenses?
Keystrokes (RPN mode) Display
fCLEARH
0.00
7000?1
7,000.00
Down payment.
30?2
30.00
Life of mortgage.
12?3
12.00
Interest rate.
110?4
110.00
Property taxes.
65?5
65.00
Monthly expenses.
1200?6
1,200.00
Closing costs.
8?7
8.00
Resale costs (as a percentage).
400?8
400.00
Rent.
6.25?9
6.25
Savings interest rate.
30?.0
30.00
Tax bracket.
fCLEARG
30.00
Clear financial registers.
4n
4.00
Years in investment.
10¼
10.00
Yearly appreciation rate.
70000$
70,000.00
House price.
t
32,391.87
NCPR (calculated).
t
19.56
Yield.
t
21,533.79
Balance in savings.
132 Section 12: Real Estate and Lending
Leases often call for periodic contractual adjustments of rental payments. For
example, a 2-year lease calls for monthly payments (at the beginning of the
month) of $500 per month for the first 6 months, $600 per month for the next 12
months, and $750 per month for the last 6 months. This situation illustrates what
is called a “step-up” lease. A “step-down” lease is similar, except that rental
payments are decreased periodically according to the lease contract. Lease
payments are made at the beginning of the period.
In the example cited, the rental payment stream for months 7 through 24 are
“deferred annuities,” as they start at some time in the future. The cash flow
diagram from the investors viewpoint looks like this:
To find today’s present value of the cash flows assuming a desired yield, the NPV
technique may be used. (Refer to pages 59 thru 63.)
Example 2: A 2-year lease calls for monthly payments (at the beginning of the
month) of $500 per month for the first 6 months, $600 per month for the next 12
months, and $750 per month for the last 6 months. If you wish to earn 13.5%
annually on these cash flows, how much should you invest (what is the present
value of the lease)?
Keystrokes (RPN mode) Display
fCLEARH
0.00
Initialize.
0gJ
0.00
First cash flow.
0gK
8ga
0.00
8.00
Second through ninth cash flows.
7000gK
4ga
7,000.00
4.00
Tenth through thirteenth cash flows.
6¼
6.00
Interest.
fl
15,218.35
NPV.
Section 12: Real Estate and Lending 133
Keystrokes Display
fCLEARH
0.00
Initialize.
500gJ
500.00
First cash flow.
gK
5ga
500.00
5.00
Second thru sixth cash flows.
600gK
12ga
600.00
12.00
Next twelve cash flows.
750gK
6ga
750.00
6.00
Last six cash flows.
13.5gC
1.13
Monthly interest rate
fl
12,831.75
Amount to invest to achieve a
13.5% yield.
134
Section 13
Investment Analysis
Partial-Year Depreciation
For both income tax purposes and financial analyses, it is valuable to calculate
depreciation based on a calendar or fiscal accounting year. When the acquisition
date of an asset does not coincide with the start of the year – which is the rule
rather than the exception – the amounts of depreciation in the first and last years
are computed as fractions of a full years depreciation.
Straight-Line Depreciation
The following HP 12C Platinum program (written in RPN mode) calculates the
straight-line depreciation for the year desired with the acquisition date occurring
at any time during the year.
KEYSTROKES
(RPN mode)
DISPLAY
KEYSTROKES
(RPN mode)
DISPLAY
fs -
021, 30
f] n
022, 11
fCLEAR
Î
000,
:0
023, 45 0
1
001, 1
gm
024, 43 35
2
002, 2
gi035
025, 43,33,035
z
003, 10
:2
026, 45 2
?1
004, 44 1
gu
027, 43 31
~
005, 34
:0
028, 45 0
?2
006, 44 2
fV
029, 42 23
1
007, 1
t
030, 31
-
008, 30
1
031, 1
?0
009, 44 0
?=0
032, 44 40 0
1
010, 1
?=2
033, 44 40 2
fV
011, 42 23
gi026
034, 43,33,026
:1
012, 45 1
:2
035, 45 2
§
013, 20
gu
036, 43 31
Section 13: Investment Analysis 135
1. Key in the program.
2. Press fCLEARG.
3. Key in the book value then press $.
4. Key in the salvage value then press M.
5. Key in the life in years (an integer) then press n.
6. Key in the year desired then press \.
7. Key in the number of months in the first year and press t.
7
The display
will show the amount of depreciation for the desired year. If desired, press
~ to see the remaining depreciable value then press :$:3=
~-:M- to find the total depreciation from the first year
through the current year.
8. Press t for the amount of depreciation and remaining depreciable value
for the next year. Repeat this step for the following years.
9. For a new case, press gi000 and return to step 2.
Note: If the number of months in the first calendar year is less than 12, the
amount of depreciation in the 1st year will be less than a full year’s
depreciation. The actual number of years that depreciation will occur is
equal to the life +1. For example, a drill has a life of 3 years and is
purchased 3 months before the year end. The following time diagram
shows that depreciation will occur over 4 calendar years.
?3
014 44 3
:$
037, 45 13
:$
015, 45 13
:M
038, 45 15
~
016, 34
-
039, 30
-
017, 30
:3
040, 45 3
$
018, 13
gi030
041, 43,33,030
:n
019, 45 11
fs
:1
020, 45 1
REGISTERS
n: Life i: Unused PV: Dep. Value PMT: Unused
FV: Salvage R
0
: Used R
1
: #Mos./12 R
2
: Counter
R
3
: 1
st
Yr. Dep.
R
4
–R
.4
: Unused
7.
The display will pause showing the year number before showing the amount of depreciation
for that year.
136 Section 13: Investment Analysis
Example 1: A property has just been purchased for $150,000. The purchase
price is allocated between $25,000 for land and $125,000 for improvements
(building). The remaining useful life of the building is agreed to be 25 years.
There is no salvage value forecasted at the end of the useful life of the building.
Thus, the depreciable value and book value is $125,000.
The building was acquired 4 months before the end of the year. Using
straight-line depreciation, find the amount of depreciation and remaining
depreciable value for the 1st, 2nd, 25th, and 26th years. What is the total
depreciation after 3 years?
Keystrokes (RPN mode) Display
fCLEARG Salvage value = 0 so FV = 0.
125000$
125,000.00
Book value.
25n
25.00
Life.
1\
1.00
Year desired.
4t
~
1.00
1,666.67
123,333.33
First year:
depreciation,
remaining depreciable value.
t
~
2.00
5,000.00
118,333.33
Second year:
depreciation,
remaining depreciable value.
t
3.00
5,000.00
Third year:
depreciation.
~:$:3
+~-
gi000
11,666.67
Total depreciation through third
year.
fCLEARG
11,666.67
125000$
125,000.00
Book value.
25n
25.00
Life.
25\
25.00
Year desired.
4t
~
25.00
5,000.00
3,333.33
Twenty-fifth year:
depreciation,
remaining depreciable value.
t
~
26.00
3,333.33
0.00
Twenty-sixth year:
depreciation,
remaining depreciable value.
Section 13: Investment Analysis 137
Example 2: A new car was purchased for $6,730 with 4½ months remaining in
the year. If the expected life of the car is 5 years, what is the amount of
depreciation in the first year?
Declining-Balance Depreciation
The following HP 12C Platinum program (written in RPN mode) calculates the
declining-balance depreciation for the year desired with the acquisition date
occurring at any time during the year.
Keystrokes (RPN mode) Display
gi000
fCLEARG
6730$
6,730.00
Book value.
5n
5.00
Life.
1\
1.00
4.5t
1.00
504.75
First year:
depreciation.
KEYSTROKES
(RPN mode)
DISPLAY
KEYSTROKES
(RPN mode)
DISPLAY
fs :0
019, 45 0
f] gm
020, 43 35
fCLEAR
Î
000,
gi031
021, 43,33,031
1
001, 1
:2
022, 45 2
2
002, 2
gu
023, 43 31
z
003, 10
:0
024, 45 0
?1
004, 44 1
f#
025, 42 25
~
005, 34
t
026, 31
?2
006, 44 2
1
027, 1
1
007, 1
?+0
028, 44 40 0
-
008, 30
?+2
029, 44 40 2
?0
009, 44 0
gi022
030,43,33,022
1
010, 1
:2
031, 45 2
f#
011, 42 25
gu
032, 43 31
:1
012, 45 1
:$
033, 45 13
§
013, 20
:M
034, 45 15
138 Section 13: Investment Analysis
1. Key in the program.
2. Press fCLEARG.
3. Key in the book value then press $.
4. Key in the salvage value then press M.
5. Key in the declining-balance factor as a percentage then press ¼.
6. Key in the life in years (an integer) then press n.
7. Key in the year desired then press \.
8. Key in the number of months in first year
8
and press t.
9
The display
will show the amount of depreciation for the desired year. Press ~ to see
the remaining depreciable value. If desired, press :$:3=
~-:M- to find the total depreciation through the current year.
9. Press t for the amount of depreciation then, if desired, press ~ for
the remaining depreciable value for the next year. Repeat this step for the
following years.
10. For a new case press gi000 and return to step 2.
Example: An electron beam welder which costs $50,000 is purchased 4 months
before the end of the accounting year. What will the depreciation be during the
first full accounting year (year 2) if the welder has a 6 year depreciable life, a
salvage value of $8,000 and is depreciated using the declining-balance
depreciation method? The declining-balance factor is 150%.
?3
014, 44 3
-
035, 30
:$
015, 45 13
:3
036, 45 3
~
016, 34
gi026
037,43,33,026
-
017, 30
fs
$
018, 13
REGISTERS
n: Life i: Factor PV: Dep. Value PMT: Unused
FV: Salvage R
0
: Used R
1
: #Mos./12 R
2
: Counter
R
3
: 1
st
Yr. Dep.
R
4
R
.4
: Unused
8.
Refer to straight-line depreciation instruction note, page 135.
9.
The display will pause showing the year number before showing the amount of depreciation
for that year.
Section 13: Investment Analysis 139
Sum-of-the-Years-Digits Depreciation
The following HP 12C Platinum program (written in RPN mode) calculates the
sum-of-the-years-digits depreciation for the year desired with the acquisition
date occurring at any time during the year.
Keystrokes (RPN mode) Display
fCLEARG
50000$
50,000.00
Book value.
8000M
8,000.00
Salvage value.
150¼
150.00
Declining-balance factor.
6n
6.00
Life.
2\
2.00
Year desired.
4t
2.00
11,458.33
Second year:
depreciation.
KEYSTROKES
(RPN mode)
DISPLAY
KEYSTROKES
(RPN mode)
DISPLAY
fs -
021, 30
f] n
022, 11
fCLEAR
Î
000,
:0
023, 45 0
1
001, 1
gm
024, 43 35
2
002, 2
gi035
025, 43,33,035
z
003, 10
:2
026, 45 2
?1
004, 44 1
gu
027, 43 31
~
005, 34
:0
028, 45 0
?2
006, 44 2
029, 42 24
1
007, 1
t
030, 31
-
008, 30
1
031, 1
?0
009, 44 0
?=0
032, 44 40 0
1
010, 1
?=2
033, 44 40 2
011, 42 24
gi026
034, 43,33,026
:1
012, 45 1
:2
035, 45 2
§
013, 20
gu
036, 43 31
140 Section 13: Investment Analysis
1. Key in the program.
2. Press fCLEARG.
3. Key in the book value then press $.
4. Key in the salvage value then press M.
5. Key in the life in years (an integer) then press n.
6. Key in the year desired then press \.
7. Key in the number of months in first year
10
then press t.
11
The display
will show the amount of depreciation for the desired year. If desired, press
~ to see the remaining depreciable value, then press :$:3=
~-:M- to find the total depreciation through the current year.
8. Press t for the amount of depreciation then, if desired, press ~ for
the remaining depreciable value for the next year. Repeat this step for the
following years.
9. For a new case press gi000 and return to step 2.
Example: A commercial movie camera is purchased for $12,000. If maintained
properly, the camera has a useful life expectancy of 25 years with $500 salvage
value. Using the sum-of-the-years-digits method, what is the amount of
depreciation and the remaining depreciable value for the 4th and 5th years?
Assume the first depreciation year is 11 months long.
?3
014, 44 3
:$
037, 45 13
:$
015, 45 13
:M
038, 45 15
~
016, 34
-
039, 30
-
017, 30
:3
040, 45 3
$
018, 13
gi030
041, 43,33,030
:n
019, 45 11
fs
:1
020, 45 1
REGISTERS
n: Life i: Unused PV: Dep. Value PMT: Unused
FV: Salvage R
0
: Used R
1
: #Mos./12 R
2
: Counter
R
3
: 1
st
Yr. Dep.
R
4
R
.4
: Unused
10.
Refer to straight-line depreciation instruction note, page 135.
11.
The display will pause showing the year number before showing the amount of depreciation
for that year.
Section 13: Investment Analysis 141
Full- and Partial-Year Depreciation with
Crossover
When calculating declining-balance depreciation it is often advantageous for tax
purposes to switch from declining balance to straight-line depreciation at some
point. This HP 12C Platinum program calculates the optimum crossover point
and automatically switches to straight-line depreciation at the appropriate time.
The crossover point is the end of the year in which the declining-balance
depreciation last exceeds or equals the amount of straight-line depreciation. The
straight-line depreciation is determined by dividing the remaining depreciable
value by the remaining useful life.
Given the desired year and the number of months in the first year, this program
calculates the depreciation for the desired year, the remaining depreciable value,
and the total depreciation through the current year.
Keystrokes (RPN mode) Display
fCLEARG
12000$
12,000.00
Book value.
500M
500.00
Salvage value.
25n
25.00
Life.
4\
4.00
Year desired.
11t
~
4.00
781.41
8,238.71
Fourth year:
depreciation,
remaining depreciable value.
t
~
5.00
746.02
7,492.69
Fifth year:
depreciation,
remaining depreciable value.
KEYSTROKES
(RPN mode)
DISPLAY
KEYSTROKES
(RPN mode)
DISPLAY
fs :4
048, 45 4
f] z
049, 10
fCLEAR
Î
000,
go
050, 43 34
1
001, 1
gi053
051, 43,33,053
2
002, 2
gi065
052, 43,33,065
z
003, 10
d
053, 33
142 Section 13: Investment Analysis
?6
004, 44 6
0
054, 0
:n
005, 45 11
:0
055, 45 0
~
006, 34
go
056, 43 34
-
007, 30
gi086
057, 43,33,086
?4
008, 44 4
:$
058, 45 13
d
009, 33
:5
059, 45 5
?0
010, 44 0
-
060, 30
1
011, 1
$
061, 13
?-0
012,44 30 0
1
062, 1
?2
013, 44 2
?-4
063, 44 30 4
?3
014, 44 3
gi040
064, 43,33,040
f#
015, 42 25
:4
065, 45 4
:6
016, 45 6
n
066, 11
§
017, 20
0
067, 0
?1
018, 44 1
?6
068, 44 6
:$
019, 45 13
1
069, 1
~
020, 34
?-2
070, 44 30 2
-
021, 30
?=0
071, 44 40 0
$
022, 13
:5
072, 45 5
\
023, 36
?-1
073, 44 30 1
gF
024, 43 40
:3
074, 45 3
~
025, 34
fV
075, 42 23
:M
026, 45 15
?+1
076, 44 40 1
-
027, 30
1
077, 1
~
028, 34
?-0
078, 44 30 0
:0
029, 45 0
?+2
079, 44 40 2
1
030, 1
?+3
080, 44 40 3
go
031, 43 34
d
081, 33
gi039
032,43,33,039
:0
082, 45 0
d
033, 33
1
083, 1
d
034, 33
go
084, 43 34
1
035, 1
gi074
085, 43,33,074
gu
036, 43 31
d
086, 33
d
037, 33
d
087, 33
Section 13: Investment Analysis 143
1. Key in the program.
2. Press fCLEARH.
3. Key in the book value then press $.
4. Key in the salvage value then press M.
5. Key in the life in years (an integer) then press n.
6. Key in the declining-balance factor as a percentage then press ¼.
7. Key in the desired year and press \.
8. Key in the number of months in the first year
12
then press t
13
to
calculate the amount of depreciation for the desired year.
9. If desired, press ~ to see the remaining depreciable value.
10. If desired, press :1 to see the total depreciation through the current
year.
11. Continue pressing t
to find the amount of depreciation for the
successive years. Steps 9 and 10 may be repeated for each year.
12. For a new case press gi000 and return to step 2.
t
038, 31
:2
088, 45 2
1
039, 1
gu
089, 43 31
?+2
040, 44 40 2
d
090, 33
?-0
041, 44 30 0
t
091, 31
f#
042, 42 25
:6
092, 45 6
?+1
043, 44 40 1
gm
093, 43 35
?5
044, 44 5
gi074
094, 43,33,074
:$
045, 45 13
gi058
095, 43,33,058
:M
046, 45 15
fs
-
047, 30
REGISTERS
n: Life i: Factor PV: Dep. Value PMT: Unused
FV: Salvage R
0
: Used R
1
: Dep. R
2
: Counter
R
3
: Used R
4
:
Used R
5
:
Used R
6
:
Used
12.
Refer to straight-line depreciation note page 135.
13.
The display will pause with the year number before displaying the amount of depreciation for
that year.
144 Section 13: Investment Analysis
Example: An electronic instrument is purchased for $11,000, with 6 months
remaining in the current fiscal year. The instrument’s useful life is 8 years and
the salvage value is expected to be $500. Using a 200% declining-balance factor,
generate a depreciation schedule for the instrument’s complete life. What is the
remaining depreciable value after the first year? What is the total depreciation
after the 7th year?
Keystrokes (RPN mode) Display
fCLEARH
0.00
11000$
11,000.00
Book value.
500M
500.00
Salvage value.
8n
8.00
Life.
200¼
200.00
Declining-balance factor.
1\
1.00
First year depreciation desired.
6t
~
1.00
1,375.00
9,125.00
First year:
depreciation,
remaining depreciable value.
t
2.00
2,406.25
Second year:
depreciation.
t
3.00
1,804.69
Third year:
depreciation.
t
4.00
1,353.51
Fourth year:
depreciation.
t
5.00
1,015.14
Fifth year:
depreciation.
t
6.00
761.35
Sixth year:
depreciation.
a
a By observation the crossover was year 6. Years 7, 8, and 9 use straight-line depreciation.
t
7.00
713.62
Seventh year:
depreciation.
:1
9,429.56
Total depreciation through the
seventh year.
t
8.00
713.63
Eight year:
depreciation
t
9.00
356.81
Ninth year:
depreciation.
Section 13: Investment Analysis 145
Excess Depreciation
When accelerated depreciation is used, the difference between total depreciation
charged over a given period of time and the total amount that would have been
charged under straight-line depreciation is called excess depreciation. To obtain
excess depreciation:
1. Calculate the total depreciation then press \.
2. Key in the depreciable amount (cost less salvage) then press \. Key in
the useful life of the asset in years then press z. Key in the number of
years in the income projection period then press § to get the total
straight-line depreciation charge.
3. Press - to get the excess depreciation.
Example: What is the excess depreciation in the previous example over 7
calendar years? (Because of the partial first year, there are 6½ years depreciation
in the first 7 calendar years.)
Modified Internal Rate of Return
The traditional Internal Rate of Return (IRR) technique has several drawbacks
which hamper its usefulness in some investment applications. The technique
implicitly assumes that all cash flows are either reinvested or discounted at the
computed yield rate. This assumption is financially reasonable as long as the rate
is within a realistic borrowing and lending range (for example, 10% to 20%).
When the IRR becomes significantly greater or smaller, the assumption becomes
less valid and the resulting value less sound as an investment measure.
IRR also is limited by the number of times the sign of the cash flow changes
(positive to negative or vice versa). For every change of sign, the IRR solution
has the potential for an additional answer. The cash flow sequence in the
example that follows has three sign changes and hence up to three potential
internal rates of return. This particular example has three positive real answers:
1.86, 14.35, and 29. Although mathematically sound, multiple answers probably
are meaningless as an investment measure.
Keystrokes (RPN mode) Display
9429.56\
9429.56
Total depreciation through seventh
year.
10500\
10,500.00
Depreciable amount.
8z
1,312.50
Yearly straight-line depreciation.
6.5§
8,531.25
Total straight-line depreciation.
-
898.31
Excess depreciation
146 Section 13: Investment Analysis
This Modified Internal Rate of Return procedure (MIRR) is one of several IRR
alternatives which avoids the drawbacks of the traditional IRR technique. The
procedure eliminates the sign change problem and the reinvestment (or
discounting) assumption by utilizing user stipulated reinvestment and borrowing
rates.
Negative cash flows are discounted at a safe rate that reflects the return on an
investment in a liquid account. The figure generally used is a short-term security
(T-Bill) or bank passbook rate.
Positive cash flows are reinvested at a reinvestment rate which reflects the return
on an investment of comparable risk. An average return rate on recent market
investments might be used.
The steps in the procedure are:
1. Calculate the future value of the positive cash flows (NFV) at the
reinvestment rate.
2. Calculate the present value of the negative cash flows (NPV) at the safe
rate.
3. Knowing n, PV, and FV, solve for i.
Example: An investor has the following unconventional investment opportunity.
The cash flows are:
Calculate the MIRR using a safe rate of 6% and a reinvestment (risk) rate of
10%.
Group # of Months Cash Flow ($)
0 1 –180,000
1 5 100,000
2 5 –100,000
39 0
4 1 200,000
Keystrokes (RPN mode) Display
fCLEARH
0.00
0gJ
0.00
First cash flow.
100000gK
5ga
5.00
Second through sixth cash flows.
0gK5ga
5.00
Next five cash flows.
0gK9ga
9.00
Next nine cash flows.
Section 13: Investment Analysis 147
200000gK
200,000.00
Last cash flow.
10gCfl
657,152.37
NPV of positive cash flows.
Þ$
20nM
775,797.83
NFV of positive cash flows.
180000ÞgJ
0gK5ga
100000ÞgK
5ga
6gCfl
-660,454.55
NPV of negative cash flows.
20
0.81
Monthly MIRR
12§
9.70
Annual MIRR.
Keystrokes (RPN mode) Display
148
Section 14
Leasing
Advance Payments
Situations may exist where payments are made in advance (leasing is a good
example). These agreements call for extra payments to be made when the
transaction is closed.
This first procedure finds the periodic payment amount necessary to achieve a
desired yield when a number of payments are made in advance. And, given the
periodic payment, the second procedure calculates the periodic yield.
Solving For Payment
To calculate the payment, information is entered as follows:
1. Press and fCLEARG.
2. Key in the total number of payments in the lease then press \.
3. Key in the total number of payments made in advance then press ?0-
n.
4. Key in or calculate the periodic interest rate as a percentage then press ¼.
5. Press 1ÞP$:0+.
6. Key in the initial loan amount then press ~z, to obtain the periodic
payment to be received by the lessor.
Example 1: Equipment worth $750 is leased for 12 months. The equipment is
assumed to have no salvage value at the end of the lease. The lessee has agreed
to make three payments at the time of closing. What monthly payment is
necessary to yield the lessor 10% annually?
Keystrokes (RPN mode) Display
fCLEARG
12\
12.00
Duration of lease.
3?0-n
9.00
Number of periodic payments.
10gC
0.83
1ÞP
–1.00
$:0+
11.64
750~z
64.45
Monthly payment to be received.
Section 14: Leasing 149
If solving for the payment amount will be done repetitively, key in the following
HP 12C Platinum program.
1. Key in the program.
2. Key in the total number of payments in the lease then press ?0.
3. Key in the total number of payments made in advance then press ?1.
4. Key in the periodic interest rate as a percentage then press ?2.
5. Key in the loan amount and press ?3; then press t to obtain the
periodic payment to be received by the lessor.
6. For a new case, return to step 2. The values changed from the previous
case are the only values which need to be entered.
KEYSTROKES
(RPN mode)
DISPLAY
KEYSTROKES
(RPN mode)
DISPLAY
fs 1
009, 1
f] Þ
010, 16
fCLEAR
Î
000,
P
011, 14
001, 43 8
$
012, 13
fCLEAR
G
002, 42 34
:1
013, 45 1
:0
003, 45 0
+
014, 40
:1
004, 45 1
:3
015, 45 3
-
005, 30
~
016, 34
n
006, 11
z
017, 10
:2
007, 45 2
fs
¼
008, 12
REGISTERS
n: n–#Adv. Pmt. i: i PV: Used PMT: –1
FV: 0 R
0
: n R
1
: #Adv. Pmt. R
2
: i
R
3
: Loan R
4
R
.7
: Unused
150 Section 14: Leasing
Example 2: Using the preceding program, solve for the monthly payment using
the information given in example 1. Then change the yearly interest to 15% and
solve for the new payment amount.
Example 3: Using the information from example 1, what monthly payment is
necessary to yield the lessor 15% annually if one payment is due at the time of
closing?
Assuming that the previous example was just solved, the keystrokes are as
follows:
Since this problem is an annuity due situation (one payment at the beginning of
the period) the calculation could also be done as follows:
Solving for Yield
To calculate the periodic yield, information is entered as follows:
1. Press and fCLEARG.
2. Key in the total number of payments in the lease then press \.
3. Key in the total number of payments made in advance then press
?0-n.
4. Key in the periodic payment to be received then press P.
Keystrokes (RPN mode) Display
12?0
12.00
Duration of lease.
3?1
3.00
Number of advance payments.
10\12z
?2
0.83
Periodic interest rate.
750?3t
64.45
Monthly payment to be received.
15\12z
?2t
65.43
Monthly payment to achieve a 15%
yield.
Keystrokes (RPN mode) Display
1?1t
66.86
Monthly payment to be received.
Keystrokes (RPN mode) Display
fCLEARG
12n15gC
1.25
Periodic interest rate (into i).
750Þ$P
66.86
Monthly payment to be received.
Section 14: Leasing 151
5. Key in the total amount of the loan then press
Þ:0:P§+$.
6. Press ¼ to obtain the periodic yield.
Example 1: A lease has been written to run for 60 months. The leased
equipment has a value of $25,000 with a $600 monthly payment. The lessee has
agreed to make 3 payments at the time of closing ($1800). What is the annual
yield to the lessor?
If solving for yield will be done repetitively, key in the following HP 12C
Platinum program:
Keystrokes (RPN mode) Display
fCLEARG
60\3
?0-n
57.00
Number of periodic payments.
600P
25000Þ:0
3.00
Number of advance payments.
:P§+$
-23,200.00
PV.
¼
1.44
Monthly yield (calculated).
12§
17.33
Annual yield (as a percentage).
KEYSTROKES
(RPN mode)
DISPLAY
KEYSTROKES
(RPN mode)
DISPLAY
fs :3
009, 45 3
f] Þ
010, 16
fCLEARÎ
000,
:1
011, 45 1
001, 43 8
:P
012, 45 14
fCLEARG
002, 42 34
§
013, 20
:0
003, 45 0
+
014, 40
:1
004, 45 1
$
015, 13
-
005, 30
¼
016, 12
n
006, 11
:gC
017, 45,43 12
:2
007, 45 2
fs
P
008, 14
152 Section 14: Leasing
1. Key in the program.
2. Key in the total number of payments in the lease then press ?0.
3. Key in the total number of payments made in advance then press ?1.
4. Key in the periodic payment to be received then press ?2.
5. Key in the total amount of the loan, then press ?3; then press t to
obtain the periodic yield.
6. For a new case, return to step 2. The values changed from the previous
case are the only values which need to be re-entered.
Example 2: Using the program, solve for yield using the same information given
in example 1. Then change the payment to $625 and solve for the yield.
Advance Payments With Residual
Situations may arise where a transaction has advance payments and a residual
value (salvage value) at the end of the normal term.
Solving for Payment
The following program solves for the periodic payment amount necessary to
achieve a desired yield.
REGISTERS
n: n–#Adv.
Pmts.
i: i PV: Used PMT: Pmt.
FV: 0 R
0
: n R
1
: Adv. Pmts. R
2
: Pmt.
R
3
: Loan R
4
R
.7
: Unused
Keystrokes (RPN mode) Display
60?0
60.00
Number of payments.
3?1
3.00
Number of advance payments.
600?2
600.00
Periodic payment.
25000?3t
17.33
Annual yield (as a percentage).
625?2t
19.48
Annual yield (as a percentage)
when PMT is increased $25.
Section 14: Leasing 153
1. Key in the program.
2. Key in the total number of payments then press ?0.
3. Key in or calculate the periodic interest rate then press ?1.
4. Key in the loan amount then press ?2.
5. Key in the residual value then press ?3.
6. Key in the total number of payments made in advance then press ?4.
Then press t to obtain the payment amount received by the lessor.
7. For a new case, return to step 2. The values changed from the previous
case are the only values which need to be re-entered.
KEYSTROKES
(RPN mode)
DISPLAY
KEYSTROKES
(RPN mode)
DISPLAY
fs M
014, 15
f] :n
015, 45 11
fCLEAR
Î
000,
:4
016, 45 4
001, 43 8
-
017, 30
fCLEAR
G
002, 42 34
n
018, 11
:0
003, 45 0
1
019, 1
n
004, 11
Þ
020, 16
:1
005, 45 1
P
021, 14
¼
006, 12
$
022, 13
:3
007, 45 3
:4
023, 45 4
M
008, 15
+
024, 40
$
009, 13
:5
025, 45 5
:2
010, 45 2
~
026, 34
+
011, 40
z
027, 10
?5
012, 44 5
fs
0
013, 0
REGISTERS
n: Used. i: Interest PV: Used PMT: –1.
FV: Residual R
0
: # Pmts (n) R
1
: Interest. R
2
: Loan.
R
3
: Residual R
4
: # Adv. Pmt. R
5
: Used R
6
–R
.6
: Unused
154 Section 14: Leasing
Example 1: A copier worth $22,000 is to be leased for 48 months. The lessee
has agreed to make 4 payments in advance, with a purchase option at the end of
48 months enabling him to buy the copier for 30% of the purchase price. What
monthly payment is necessary to yield the lessor 15% annually:
Example 2: Using the information from example 1, what would the monthly
payments be if the lessor desired a yield of 18% annually?
Solving For Yield
Solving for yield is essentially the same as solving for Internal Rate of Return
(IRR). The keystrokes are as follows:
1. Press fCLEARH.
2. Key in the amount of the first cash flow then press gJ. This initial
amount is the difference between the initial loan amount and any payments
received at closing time. Observe the sign convention: positive for cash
received and negative for cash paid out.
3. Key in the amount of the first cash flow then press gK. Then key in
the number of times that cash flow occurs then press ga.
Keystrokes (RPN mode) Display
48?0
15\
12z?1
1.25
Monthly interest rate.
22000?2
30b?3
4?4t
487.29
Monthly payment received by
lessor.
Keystrokes (RPN mode) Display
487.29
From previous example.
18\12z
1.50
Monthly interest rate.
?1t
520.81
Monthly payment received by
lessor.
Section 14: Leasing 155
4. Key in 0gK then the number of advance payments minus one. Then
press ga.
5. Key in the residual then press gK. Then press fL to solve for
periodic yield.
Example: Equipment worth $5000 is leased for 36 months at $145 per month.
The lessee has agreed to pay the first and last month’s payments in advance. At
the end of the lease, the equipment may be purchased for $1500. What is the
annual yield to the lessor if the equipment is purchased?
Keystrokes (RPN mode) Display
fCLEARH
5000Þ\
145\2
§=gJ
–4,710.00
Net amount of cash advanced.
145gK34ga
34.00
Thirty-four cash flows of $145.00.
0gK
0.00
Thirty-fifth cash flow.
1500gK
1,500.00
Thirty-sixth cash flow.
fL12§
18.10
Annual yield to lessor.
156
Section 15
Savings
Nominal Rate Converted to Effective Rate
Given a nominal interest rate and the number of compounding periods per year,
this keystroke procedure computes the effective annual interest rate.
1. Press and fCLEARG.
2. Key in the annual nominal rate as a percentage, then press \.
3. Key in the number of compounding periods per year, then press nz¼.
4. Key in 100 then press Þ\$.
5. Press M+ to obtain the effective annual interest rate.
Example 1: What is the effective annual interest rate if the annual nominal rate
of 5¼% is compounded quarterly?
For repeated calculations, the following HP 12C Platinum program can be used:
Keystrokes (RPN mode) Display
fCLEARG
5.25\
5.25
Nominal rate.
4nz¼
1.31
Percent quarterly interest rate.
100Þ\
$M+
5.35
Percent effective interest rate.
KEYSTROKES
(RPN mode)
DISPLAY
KEYSTROKES
(RPN mode)
DISPLAY
fs 0
007, 0
f] 0
008, 0
fCLEAR
Î
000,
Þ
009, 16
001, 43 8
\
010, 36
fCLEAR
G
002, 42 34
$
011, 13
n
003, 11
M
012, 15
z
004, 10
+
013, 40
Section 15: Savings 157
1. Key in the program.
2. Key in the annual nominal rate as a percentage then press \.
3. Key in the number of compounding periods per year then press t to
obtain the effective annual interest rate.
4. For a new case return to step 2.
Example 2: What is the effective annual rate of interest if the annual nominal
rate of 5¼% is compounded monthly?
Effective Rate Converted to Nominal Rate
Given an effective interest rate and the number of compounding periods per year,
this routine calculates the nominal interest rate.
1. Press fCLEARG.
2. Key in the number of periods per year then press n.
3. Key in 100 then press \$.
4. Key in the effective annual rate as a percentage then press +ÞM¼.
5. Press :n§ to obtain the annual nominal rate.
Example: Find the nominal rate if the effective annual rate is 5.35%
compounded quarterly.
¼
005, 12
fs
1
006, 1
REGISTERS
n: # Periods. i: Nom. Rate/n PV: 0 PMT: Used.
FV: Eff. Rate R
0
–R.
9
: Unused
Keystrokes (RPN mode) Display
5.25\
12t
5.38
Percent effective interest rate.
Keystrokes (RPN mode) Display
fCLEARG
4n100\$
100.00
5.35
–105.35
1.31
:n§
5.25
Percent nominal interest rate.
158 Section 15: Savings
Nominal Rate Converted to Continuous Effective
Rate
This procedure converts a nominal annual interest rate to the continuous
effective rate.
1. Press 1\.
2. Key in the nominal rate as a percentage then press b.
3. Press g>à.
Example: What is the effective rate resulting from a 5¼% passbook rate with
continuous compounding?
Keystrokes (RPN mode) Display
1\5.25b
g>
1.05
à
5.39
Continuous rate.
159
Section 16
Bonds
30/360 Day Basis Bonds
A bond is a contract to pay interest, usually semiannually, at a given rate
(coupon) and to pay the principal of the bond at some specified future date. A
bond which is calculated on a 30/360 day basis is one in which the day count
basis is computed using 30 days in a month and 360 days in a year.
The following program solves for the price given the yield or for the yield given
the price of a semiannual coupon bond which is calculated on a 30/360 day basis
and is held for more than six months.
KEYSTROKES
(RPN mode)
DISPLAY
KEYSTROKES
(RPN mode)
DISPLAY
fs -
023, 30
f] :6
024, 45 6
fCLEARÎ
000,
§
025, 20
fCLEARG
001, 42 34
:0
026, 45 0
002, 43 7
gm
027, 43 35
:2
003, 45 2
gi039
028, 43,33,039
2
004, 2
2
029, 2
z
005, 10
z
030, 10
P
006, 14
¼
031, 12
?6
007, 44 6
$
032, 13
:5
008, 45 5
Þ
033, 16
+
009, 40
~
034, 34
M
010, 15
-
035, 30
:3
011, 45 3
gF
036, 43 40
:4
012, 45 4
~
037, 34
013, 43 26
gi000
038, 43,33,000
d
014, 33
d
039, 33
1
015, 1
:1
040, 45 1
8
016, 8
+
041, 40
0
017, 0
Þ
042, 16
160 Section 16: Bonds
1. Key in the program.
2. If the C status indicator is not displayed, press .
3. Key in the annual coupon interest rate as a percentage then press ?2.
4. Key in the settlement date (MM.DDYYYY)
14
then press ?3.
5. Key in the maturity date (MM.DDYYYY)
then press ?4.
6. Key in the redemption value as a percentage of par then press ?5.
7. If price is desired:
a. Key in the desired yield to maturity as a percentage then press ?0.
b. Press t to calculate price as a percentage of par value.
c. Press ~ to display accrued interest due the seller.
For a new case return to step 3. Note that only those values which have been
changed need to be reentered and stored.
8. If yield is desired:
a. Press 0?0.
b. Key in the price as a percentage of par value and press ?1.
c. Press t to compute annual yield to maturity.
For a new case return to step 3. Note that only those values which have
been changed need to be reentered and stored.
z
018, 10
$
043, 13
n
019, 11
¼
044, 12
gT
020, 43 24
2
045, 2
1
021, 1
§
046, 20
~
022, 34
fs
REGISTERS
n: days/180 i: Yield/2 PV: Price PMT: Coupon/2.
FV: Red + Cpn./2 R
0
: Yield R
1
: Price. R
2
: Coupon
R
3
: D
set
R
4
: D
mat
R
5
: Redemption R
6
: Coupon/2.
R
7
–R
.3
: Unused
14.
For information about date format see pages 30 to 31.
Section 16: Bonds 161
Example 1: What price should you pay on August 28, 2003 for a 5½% bond
(computed with a 30/360 basis) that matures on June 1, 2007, if you want a yield
of 7¾%? What price should you pay for a yield of 8%? This problem assumes a
redemption value of 100.
Example 2: The market is quoting 93
3
/8% for the bond described in example 1.
What yield will that provide? What would be the yield to maturity if 92% were
the quoted price?
Annual Coupon Bonds
For bonds which have annual coupons, use the following HP 12C Platinum
program to evaluate price and accrued interest on an Actual/ Actual day basis.
This program may be modified for annual coupon bonds to be calculated on a 30/
360 day basis.
Keystrokes (RPN mode) Display
Set compound interest mode if the
C indicator is not on.
5.5?2
5.50
Coupon into register 2.
8.282003?3
8.28
Settlement date into register 3.
6.012007?4
6.01
Maturity date into register 4.
100?5
100.00
Redemption value into register 5.
7.75?0
7.75
Yield into register 0.
t
92.77
Price (calculated).
~
1.33
Accrued interest (calculated).
8?0
8.00
New yield into register 0.
t
92.01
Price to yield 8% (calculated).
~
1.33
Accrued interest (calculated).
+
93.34
Total price paid.
Keystrokes (RPN mode) Display
93.34
From previous example.
0?0
3\8z
93+?1t
7.55
Yield at 93
3
/8% (calculated).
92?1t
8.00
Yield at 92% (calculated).
162 Section 16: Bonds
KEYSTROKES
(RPN mode)
DISPLAY
KEYSTROKES
(RPN mode)
DISPLAY
fs :5
018, 45 5
f]
019, 43 26
fCLEAR
Î
000,
?7
020, 44 7
fCLEAR
G
001, 42 34
:6
021, 45 6
002, 43 8
:4
022, 45 4
:0
003, 45 0
023, 43 26
n
004, 11
:7
024, 45 7
:2
005, 45 2
z
025, 10
P
006, 14
n
026, 11
:1
007, 45 1
0
027, 0
¼
008, 12
P
028, 14
:3
009, 45 3
M
029, 15
M
010, 15
Þ
030, 16
$
011, 13
:n
031, 45 11
:5
012, 45 5
:2
032, 45 2
Æ
013, 26
Þ
033, 16
6
014, 6
§
034, 20
Þ
015, 16
t
035, 31
-
016, 30
-
036, 30
?6
017, 44 6
fs
REGISTERS
n: Used i: Yield PV: Used PMT: Cpn. or 0
FV: Used R
0
: # Periods (n) R
1
: Yield R
2
: Coupon
R
3
: Redemption R
4
: Settlement R
5
: Next Cpn. R
6
: Last Coupon
R
7
: Used R
8
–R
.5
: Unused
Section 16: Bonds 163
For annual coupon bonds calculated on a 30/360 day basis, insert d after
at steps 19 and 23 (making the program two steps longer).
1. Key in the program and press if the C status indicator is not
displayed.
2. Key in the total number of coupons which are received and press ?0.
3. Key in the annual yield as a percentage then press ?1.
4. Key in the amount of the annual coupon then press ?2.
15
5. Key in the redemption value then press ?3.
15
6. Key in the settlement (purchase) date
16
then press ?4.
7. Key in the date† of the next coupon then press ?5.
8. Press t to obtain the amount of accrued interest.
9. Press t to determine the price of the bond.
10. For a new case, return to step 2.
Example: What is the price and accrued interest of a 20-year Eurobond with
annual coupons of 6.5% purchased on August 15, 2003 to yield 7%. The next
coupon is received on December 1, 2003.
15.
Positive for cash received; negative for cash paid out.
16.
For information about date format see pages 30 to 31.
Keystrokes (RPN mode)
Display
Set compound interest mode if the
C indicator is not on.
20?0
20.00
Total number of coupons.
7?1
7.00
Annual yield.
6.5?2
6.50
Annual coupon rate.
100?3
100.00
Redemption value.
8.152003?4
8.15
Settlement date.
12.012003?5
12.01
Next coupon date.
t
–4.58
Accrued interest.
t
–94.75
Purchase price.
Appendixes
166
Appendix A
RPN and the Stack
In RPN mode, four special registers in the HP 12C Plati-
num are used for storing numbers during calculations. To
understand how these registers are used, they should be
visualized as stacked on top of each other. (For this rea-
son, they are generally referred to as the “stack registers”
or collectively as “the stack.”) The stack registers are
designated X, Y, Z, and T. Unless the calculator is in Pro-
gram mode, the number shown in the display is the number in the X-register
(modified according to the current display format).
The number in the X-register – and, for two-number functions, the number in the
Y-register – are the number(s) used in calculations. The Z- and T-registers are
used primarily for the automatic retention of intermediate results during chain
calculations, as described in section 1.
Before we discuss the details of the stack operation, let’s take a quick look at
how the stack is used in a simple arithmetic calculation and in a chain calcula-
tion. For each key pressed in the keystroke sequence, the diagram illustrating the
calculation shows, above the key, the numbers in each of the stack registers after
that key is pressed.
First, let’s consider the calculation of 5 – 2:
The diagram shows why we said in section 1 that the \ key separates the sec-
ond number entered from the first number entered. Note also that this positions
the 5 in the Y-register above the 2 in the X-register – just like they would be
positioned if you wrote the calculation vertically on paper:
Appendix A: RPN and the Stack 167
Now let’s see what happens in the stack during a chain calculation in RPN mode:
See how the intermediate results are not only displayed when they are calculated,
but also automatically stored and available in the stack at just the right time!
That’s basically how the stack operates. In the rest of this appendix, we’ll take a
more detailed look at how numbers are entered into and rearranged within the
stack, and the effect of the various HP 12C Platinum functions on the numbers in
the stack.
Getting Numbers Into the Stack: The \ Key
As discussed in earlier sections, if two numbers are being keyed in for a
two-number function – such as + – you press \ between the numbers to
separate them. The following diagram illustrates what happens in the stack when
you enter the numbers 10 and 3 (to calculate, for example, 10 ÷ 3). (Assume that
the stack registers have been already loaded with the numbers shown as the
result of previous calculations).
When a digit is keyed into the display, it is simultaneously entered into the
X-register. As additional digit keys are pressed, the corresponding digits are
appended (that is, added to the right of) those already in the displayed X-register
until \ is pressed. As shown in the preceding diagram, pressing \ does the
following:
1. It copies the number from the displayed X-register into the Y-register. This
process is part of the stack lift.
2. It tells the calculator that the number in the displayed X-register is
complete: that is, it terminates digit entry.
34×()56×()+
7
----------------------------------------
168 Appendix A: RPN and the Stack
Termination of Digit Entry
The first digit keyed in after digit entry has been terminated replaces the number
already in the displayed X-register. Digit entry is automatically terminated when
any key is pressed (except for digit entry keys – digit keys,., Þ, and É
and prefix keys – f, g,?, :, and i).
Stack Lift
When the stack lifts, the number in each stack register is copied into the register
above, and the number formerly in the T-register is lost. The number formerly in
the X-register is then contained in both the X-register and the Y-register.
When a number is entered into the displayed X-register – either from the key-
board, from a storage register (using:), or from the LAST X register (using
F) – the stack usually lifts first. The stack does not lift if the last key pressed
before a number is entered was one of the following: \, O, _, ^, A
or C.
1
If one of these keys was the last key pressed, the number in the dis-
played X-register is replaced when a new number is entered.
Rearranging Numbers in the Stack
The ~ Key
Pressing ~ exchanges the numbers in the X- and
Y-registers.
Certain functions (Ò, Ï, !, E, V,
Ý, #, Ö, v, R, and Q) return answers to
the Y-register as well as to the displayed X-register. The ~ key, since it
exchanges the number in the Y-register with that in the displayed X-register, is
used to display the second number calculated.
The d Key
When d (roll down) is pressed, the number in each
stack register is copied into the register below, and
the number formerly in the X-register is copied into
the T-register.
1.
In addition, the stack does not lift when a number is entered if the last operation performed
was storing a number into a financial register. For example, the stack will not lift when a
number is entered following the sequence 100000$, but will lift when a number is entered
following the sequence 100000$M. Note also that although the stack lifts when \ is
pressed, it does not lift when a number is entered after \ is pressed.
Appendix A: RPN and the Stack 169
Pressing d four times successively displays the numbers in the Y-, Z-, and
T-registers and returns the numbers to their original registers.
One-Number Functions and the Stack
One-number mathematics and number-alteration functions – y, r, ¿ >,
e, B, Ñ, and T – use only the number in the displayed X-register.
When the key is pressed, the function is performed upon the number in the
X-register, and the answer is then placed into the X-register. The stack does not
lift, so the number formerly in the X-register does not get copied into the Y-
register; but this number is copied into the LAST X register. The numbers in the
Y-, Z-, and T-registers are not affected when a one number function is per-
formed.
Two-Number Functions and the Stack
Two-number functions – +, -, §, z, q, b, à, and Z – use the
numbers in both the X- and the Y-registers.
Mathematics Functions
To perform an arithmetic operation, the numbers are positioned in the X- and
Y-registers just as you would write them vertically on paper: the number you
would write on top goes in the Y-register, and the number you would write on the
bottom goes in the X-register. For example, to do each of the four arithmetic
170 Appendix A: RPN and the Stack
calculations shown below, you would put the 8 in the Y-register (using \ and
then key the 2 into the displayed X-register.
When an arithmetic operation or q is performed, the answer is placed in the
X-register, the number formerly in the X-register is copied into the LAST X reg-
ister, and the stack drops. When the stack drops, the number in the Z-register is
copied into the Y-register, and the number in the T-register is copied into the Z-
register but also remains in the T-register.
The diagram on the next page illustrates the stack operation when 8 ÷ 2 is calcu-
lated. (Assume that the stack and LAST X registers have already been loaded
with the numbers shown as the result of previous calculations.)
Percentage Functions
When any of the three percentage functions is performed, the answer is placed in
the X-register, the number formerly in the X-register is copied into the LAST X
register, but the stack does not drop. The numbers in the Y-, Z-, and T-registers
are not changed when a percentage function is performed.
Appendix A: RPN and the Stack 171
Calendar and Financial Functions
The following table shows what quantity is in each stack register after the indi-
cated calendar or financial function key is pressed. The symbols x, y, z, and t rep-
resent the number that was in the corresponding register (X, Y, Z, or T,
respectively) at the time the function key was pressed.
Register
Ï
n, ¼, $,
P, M,
l, L
a
aFor n, ¼, $, P, and M, the stack registers hold the quantities
shown if the key is pressed to calculate the corresponding quantity rather
than to merely store a number in the corresponding register.
!
T ttx t y
Z
tz
INT
365
z
x (number of
payments)
Y
z
DYS
30-day
–PV y
PMT
PRIN
X
DATE
DYS
actual
INT
360
n, i, PV, PMT,
FV, NPV, IRR
PMT
INT
Register
ESV, Ý,#
T y (settlement date) zy
Z x (maturity date) y (settlement date) x (number of year)
Y
INT x (maturity date)
RDV (remaining
depreciable value)
X PRICE YTM DEP
172 Appendix A: RPN and the Stack
The LAST X Register and the F KEY
The number in the displayed X-register is copied into the LAST X register when-
ever any of the following function keys is pressed:
Pressing gF lifts the stack (unless \, O, _, ^, A, or C was
the last key pressed, as described on page 168), then copies the number from the
LAST X register into the displayed X-register. The number remains also in the
LAST X register.
Chain Calculations in RPN Mode
The automatic stack lift and stack drop make it possible to do chain calculations
without the necessity for keying in parentheses or storing intermediate results, as
are required on some other calculators. An intermediate result in the displayed
X-register is automatically copied into the Y-register when a number is keyed in
after a function key is pressed.
2
Therefore, when a two-number function key is
then pressed, that function is performed using the number keyed into the dis-
played X-register and the intermediate result in the Y-register. The number then
in the Y-register, if remaining as an intermediate result from an earlier calcula-
tion, can then be used with the intermediate result in the X-register for another
calculation.
+-§zy
q>¿rB
TÑ_^Q
RebàZ
2.
Except for \, O, _, ^, A, C, and – under certain circumstances – n, ¼,
$, P, and M. For more information, refer to Stack Lift, page 168.
Appendix A: RPN and the Stack 173
The diagram on page 167 illustrates how the automatic stack lift and stack drop
make chain calculations quick and error-free.
Virtually every chain calculation you are likely to encounter can be done using
only the four stack registers. However, to avoid having to store an intermediate
result in a storage register, you should begin every chain calculation at the inner-
most number or pair of parentheses and then work outward – just as you would if
you were doing the calculation manually (that is, using pencil and paper). For
example, consider the calculation of
3 [4 + 5 (6 + 7)]
If this calculation were done from left to right – as were the (simpler) examples
under Chain Calculations on pages page 21 and page 22 – you would have to
enter five numbers into the calculator before doing the first operation possible (6
+ 7). But since the stack holds only four numbers, this calculation cannot be
done left-to-right. However, it can easily be done if you begin with the calcula-
tion in the innermost pair of parentheses – again, (6 + 7).
Arithmetic Calculations with Constants
Because the number in the T-register remains there when the stack drops, this
number can be used as a constant in arithmetic operations. To place the constant
into the T-register, key it into the display (that is, into the X-register), then press
\ three times. This also places the constant in the Y- and Z-registers. Each
time an arithmetic operation is then performed – using the constant in the Y-reg-
ister and a number keyed into the displayed X-register – the constant will be
“dropped” back into the Y-register.
Example: The annual sales of solar engineering hardware your firm – currently
$84,000 – are projected to double each year for the next 3 years. Calculate the
annual sales for each of those years.
Keystrokes (RPN mode) Display
6\7+
13.00
Intermediate result of (6+7).
5§
65.00
Intermediate result of 5 (6+7).
4+
69.00
Intermediate result of [4 + 5(6 + 7)].
3§
207.00
Final result: 3 [4 + 5 (6 + 7)].
174 Appendix A: RPN and the Stack
In the example above, the constant was repeatedly multiplied by the result of the
previous operation, which was already in the displayed X-register. In another
class of calculations with constants, the constant is multiplied by (or added to,
etc.) a new number keyed into the displayed X-register. For these calculations,
you must press O before keying in a new number after having pressed an
operator key. If this were not done, the stack would lift when you keyed in a new
number after pressing the operator key, and the Y-register would no longer con-
tain the constant. (Recall – from page 168 – that the stack does not lift when a
number is keyed into the displayed X-register after O is pressed.)
Example: At Permex Pipes a certain pipe fitting is packaged in quantities of 15,
75, and 250. If the cost per fitting is $4.38, calculate the cost of each package.
3
Keystrokes (RPN mode) Display
2\\
\
2.00
Enters constant into Y-, Z-, and
T-registers.
84000
84,000.
Enters base amount into displayed
X-register.
§
168,000.00
Annual sales after first year.
§
336,000.00
Annual sales after second year.
§
672,000.00
Annual sales after third year.
3.
You may want to compare this method of arithmetic calculations with constants to the
method using F
described on page 74.
Keystrokes (RPN mode) Display
4.38\\
\
4.38
Enters constant into Y-, Z-, and
T-registers.
15
15.
Enters first quantity into displayed
X-register.
§
65.70
Cost of a package of 15.
O75
75.
Clears display and enters second
quantity into displayed X-register.
§
328.50
Cost of a package of 75.
O250
250.
Clears display and enters third
quantity into displayed X-register.
§
1,095.00
Cost of a package of 250.
175
Appendix B
Algebraic Mode (ALG)
To select algebraic mode, press f[. When the calculator is in algebraic
mode, the ALG status indicator is lit.
Simple Arithmetic calculations in ALG mode
To calculate 21.1 + 23.8:
Once a calculation has been completed:
z pressing another digit key starts a new calculation, or
z pressing an operator key continues the calculation.
You can also do long calculations without pressing } after each intermediate
calculation: just press it at the end. The operators perform from left to right, in
the order you enter them.
Keying in Negative Numbers (Þ)
The Þ key changes the sign of a number.
z To key in a negative number, type that number and then press Þ.
z To change the sign of an already displayed number (it must be the
rightmost number), press Þ.
Keystrokes (ALG mode) Display
21.1+
21.10
23.8
23.80
}
44.90
} completes the calculation.
Keystrokes (ALG mode) Display
77.35-
77.35
90.89}
–13.54
} completes the calculation.
65gr§12}
96.75
New calculation:
z3.5}
27.64
Calculates 96.75 ÷ 3.5
Keystrokes (ALG mode) Display
75Þ
–75
Changes the sign of 75
§7.1}
–532.50
Multiplies –75 by 7.1
65 12×
176 Appendix B: Algebraic Mode (ALG)
Chain Calculations in ALG mode
To do a chain calculation, you don’t need to press } after each operation, but
only at the very end.
For instance, to calculate you can enter either:
z 750 § 12 } z 360 } or
z 750 § 12 z 360 }
In the second case, the z key acts like the } key by displaying the result of
750 × 12.
Here’s a longer chain calculation:
This calculation can be written as: 456 – 75 ÷ 18.5 × 68 ÷ 1.9. Watch what hap-
pens in the display as you key it in:
Percentage Functions
In most cases, b divides a number by 100.
The one exception is when a plus or minus sign precedes the number.
For instance, 25 b results in 0.25.
To find 25% of 200, press: 200 § 25 b}. (Result is 50.00.)
You can calculate a net amount all in one calculation:
For instance, to decrease 200 by 25%, just enter 200-25b}. (Result is
150.00.)
Example: You borrow $1,250 from a relative, and agree to repay the loan in a
year with 7% simple interest. How much money will you owe?
Keystrokes (ALG mode) Display
456-75z
381.00
18.5§
20.59
68z
1,400.43
1.9}
737.07
Keystrokes (ALG mode) Display
1250+7b
87.50
Interest on the loan is $87.50.
}
1337.50
You owe this amount at the end of
one year.
750 12×
360
---------------------
456 75
18.5
---------------------
68
1.9
-------
×
Appendix B: Algebraic Mode (ALG) 177
Percent Difference
To find the percent difference between two numbers:
1. Key in the base number.
2. Press } to separate the other number from the base number.
3. Key in the other number.
4. Press à.
Example: Yesterday your stock fell from 35.5 to 31.25 per share. What is the
percent change?
Percent of Total
To calculate what percentage one number is of another:
1. Calculate the total amount by adding all individual amounts.
2. Key in the number whose percentage equivalent you wish to find.
3. Press Z.
Example: Last month, your company posted sales of $3.92 million in the U.S.,
$2.36 million in Europe, and $1.67 million in the rest of the world. What per-
centage of the total sales occurred in Europe?
Keystrokes (ALG mode) Display
35.5}
35.50
Keys in the base number and
separates it from the other number.
31.25
31.25
Keys in the other number.
à
11.97
Nearly a 12% decrease.
Keystrokes (ALG mode) Display
3.92+
3.92
Keys in the first number.
2.36+
6.28
Adds the second number.
1.67}
7.95
Adds the third number to get the
total.
2.36
2.36
Keys in 2.36 to find out what
percentage it is of the number in the
display.
Z
29.69
Europe had nearly 30% of the total
sales.
178 Appendix B: Algebraic Mode (ALG)
The Power Function
Pressing q calculates a power of a number, that is, y
x
. Like the arithmetic
function +, q requires two numbers:
1. Key in the base number (which is designated by the y on the key).
2. Press q and key in the exponent (which is designated by the x on the key)
3. Press } to calculate the power.
To Calculate Keystrokes (ALG mode) Display
2
1.4
2q1.4}
2.64
2
–1.4
2q1.4Þ}
0.38
(–2)
3
2Þq3}
–8.00
or 2
1/3
2q3y}
1.26
2
3
179
Appendix C
More About L
Given a sequence of positive and negative cash flows, we hope that there is
enough information to determine whether an IRR answer exists, and what that
answer is. For the vast majority of cases, your HP 12C Platinum will find the
unique IRR answer if it exists. But the IRR computation is so complex that if the
cash flow sequence does not meet certain criteria, then sometimes the calculator
is unable to determine whether or not an answer or answers exist.
Let’s look at all of the possible outcomes of IRR as calculated by your HP 12C
Platinum:
Case 1: A positive answer. If a positive answer is displayed, it is the only such
answer. One or more negative answers may also exist.
Case 2: A negative answer. If a negative answer is displayed, there may be addi-
tional negative answers, and there may be a single positive answer. If additional
answers (negative or positive) exist, they can be calculated using the procedure
described below.
Case 3: The calculator displays Error 3. This indicates that the computation is
very complex, possibly involving multiple answers, and cannot be continued
until you give the calculator an estimate of IRR. The procedure for doing so is
described below.
Case 4: The calculator displays Error 7. This indicates that there is no answer to
the computation of IRR with the cash flow amounts you have entered. This situa-
tion is probably the result of a mistake in entering the magnitudes or signs of the
cash flows or the number of times a cash flow amount occurs consecutively.
Refer to Reviewing Cash Flow Entries (page 64) and Changing Cash Flow
Entries (page 66) to check and correct the entries. Error 7 will result if there is
not at least one positive cash flow and at least one negative cash flow.
Although the calculator will eventually reach one of the above outcomes, it may
take a long time to get there. You may wish to terminate the IRR iterative pro-
cess, by pressing any key, to see what interest rate the calculator has computed at
that point. If you stop the calculation, you may continue searching for IRR as
described below.
Searching for IRR. You can continue searching for IRR solutions, even after an
Error 3 indication, as follows:
1. Make a guess for the interest rate and key it in.
2. Press:gt.
180 Appendix C: More About L
Your guess will aid the calculator in its search, and if it finds an IRR answer near
your guess, that answer will be displayed. Since the calculator cannot tell you the
number of solutions that exist when there is more than one mathematically cor-
rect answer, you can continue to make guesses, pressing :gt after each
one, to search for IRR solutions.
You can hasten this process by using the l function to help you make a good
guess. Remember that a correct IRR solution will make the calculated NPV very
small. So continue to guess interest rates and solve for NPV until the answer you
obtain is reasonably close to zero. Then press :gt to calculate the IRR
answer near your guess.
How would this work in case 2 above? The calculator displays a negative answer
and you wish to check for a unique positive IRR. Key in successively larger
guesses for i (starting from 0) and solve for NPV until you reach a sign change in
your NPV outcomes. Then press :gt to find an IRR solution near the
last interest rate obtained using the l key.
If you stop the IRR iterative process, you can test the interest obtained using
l, and then restart the process by pressing :gt.
181
Appendix D
Error Conditions
Some calculator operations cannot be performed under certain conditions (for
example, z when x = 0). If you attempt such an operation under these condi-
tions, the calculator will display the word Error followed by a digit, 0 through 9.
Listed below are operations that cannot be performed under the conditions spec-
ified. The symbols x and y represent the number in the X- and Y-registers,
respectively, when the operation key is pressed.
Error 0: Mathematics
Error 1: Storage Register Overflow
Operation Condition
z x = 0
y x = 0
r x < 0
° x 0
q y = 0 and x 0
y < 0 and x is noninteger.
à y = 0
Z y = 0
?z(0 through 4) x = 0
e x is noninteger
x < 0
Operation Condition
?+(0 through 4)
?-(0 through 4)
(0 through 4)
?z(0 through 4)
A
Magnitude of result is
greater than 9.999999999
× 10
99
.
182 Appendix D: Error Conditions
Error 2: Statistics
Error 3: IRR
Refer to Appendix C.
Error 4: Memory
z Attempting to enter more than 400 program lines.
z Attempting to i to a program line that does not exist.
z Attempting storage register arithmetic in R
5
through R
9
or R
.0
through R
.9
.
Error 5: Compound Interest
Operation Condition
Ö n (number in R
1
) = 0
h Σx = 0
v n = 0
n = 1
nΣx
2
– (Σx)
2
< 0
nΣy
2
– (Σy)
2
< 0
R n = 0
nΣx
2
– (Σx)
2
= 0
Q n = 0
nΣy
2
– (Σy)
2
= 0
R~
Q~
[nΣx
2
– (Σx)
2
][nΣy)
2
Σy)
2
)] 0
Operation Condition
n PMT PV × i
PMT = FV × i
i < –100
The values in i, PV, and FV are such that
no solution exists for n.
¼ PMT = 0 and n < 0
Cash flows all have same sign.
$ i < –100
Appendix D: Error Conditions 183
Error 6: Storage Registers
Error 7: IRR
Refer to Appendix C.
P n = 0
i = 0
i < –100
When calculating YTM or BOND PRICE
and PMT is negative.
M i < –100
! x 0
x is noninteger.
l i < –100
V
Ý
#
n 0
n > 10
10
x 0
x is noninteger
E PMT < 0
S PMT < 0
Operation Condition
?
:
Storage register specified does not exist or
has been converted to program lines.
K
a
n specifies a storage register that does not
exist or has been converted to program
lines.
l
L
n > 30
n > r (as defined by N)
n < 0
n is noninteger
a x > 99
x < 0
x is noninteger
Attempted to input N
j
for CF
0
184 Appendix D: Error Conditions
Error 8: Calendar
Error 9: Service
Refer to Appendix F.
Pr Error
z Continuous Memory has been reset. (Refer to Continuous Memory,
page 70.)
z You have reset the calculator using the reset hole (see page 196).
Operation Condition
Ò
D
Improper date format or illegal date.
D Attempting to add days beyond calcula-
tors date capacity.
E
S
Improper date format or illegal date.
More than 500 years between settlement
(purchase) date and maturity (redemption)
date.
Maturity date earlier than settlement date.
Maturity date has no corresponding cou-
pon date (6 months earlier).
a
a This is the case for the 31st of March, May, August, October, and December,
plus August 29 (except in a leap year) and 30. For example, there is no Septem-
ber 31, so March 31 has no corresponding coupon date 6 months earlier.
To correct this problem for all maturity dates except August 29 and 30, add one
day to both the settlement date and the maturity date in your calculations. For
instance, if a bond were purchased on June 1, 2003 (the settlement date) with a
maturity date of December 31, 2005, you should change the dates to June 2,
2003 and January 1, 2006 for your calculations.
For August 29 and 30, there is no calculator solution that gives the correct
answer.
185
Appendix E
Formulas Used
Percentage
% =
% =
%T =
Interest
Simple Interest
I
360
=
I
365
=
Compound Interest
Without an odd period:
0 =
n = number of compounding periods.
i = periodic interest rate, expressed as a decimal.
PV = present value.
FV = future value or balance.
PMT = periodic payment.
S = payment mode factor (0 or 1) indicating treatment
of PMT. 0 corresponds to End, 1 to Begin.
I = interest amount.
INTG (n) = integer portion of n.
FRAC (n) = fractional portion of n.
Base x() Rate x()×
100
----------------------------------------------
100
NewAmount x() Base y()
Base y()
--------------------------------------------------------------------


100
Amount x()
Total y()
-----------------------------


n
360
---------
PV i××
n
365
---------
PV× i×
PV 1 iS+()PMT
11i+()
n
i
------------------------------
FV 1 i+()
n
+⋅⋅+
186 Appendix E: Formulas Used
With simple interest used for an odd period:
0 =
With compound interest used for an odd period:
0 =
Amortization
ΣINT =
ΣPRN =
PV
n
=
n = number of payment periods to be amortized.
INT
j
= amount of PMT applied to interest in period j.
PRN
j
= amount of PMT applied to principal in period j.
PV
j
= present value (balance) of loan after payment in
period j.
j = period number.
INT
1
= {0 if n = 0 and payment mode is set to Begin.
|PV
0
× i|
RND
(sign of PMT)
PRN
1
= PMTINT
1
PV
1
= PV
0
+ PRN
1
INT
j
=|PV
j –1
× i|
RND
× (sign of PMT) for j > 1.
PRN
j
= PMTINT
j
PV
j
= PV
j –1
+ PRN
j
PV 1 iFRAC n()+[]1 iS+()PMT
11i+()
INTG n()
i
----------------------------------------------
FV 1 i+()
INTG n()
++
PV 1 i+()
FRAC n()
1 iS+()PMT
11i+()
INTG n()
i
----------------------------------------------
FV 1 i+()
INTG n()
++
INT
j
j
1=
n
INT
1
INT
2
INT
n
+++=
PRN
j
j
1=
n
PRN
1
PRN
2
PRN
n
+++=
PV
0
PRN
+
Appendix E: Formulas Used 187
Discounted Cash Flow Analysis
Net Present Value
NPV =
Internal Rate of Return
0 =
Calendar
Actual Day Basis
DYS = f(DT
2
) – f(DT
1
)
where
f(DT) = 365 (yyyy) + 31 (mm – 1) + dd + INTG (z/4) – x
and
for mm 2
x = 0
z = (yyyy) – 1
for mm > 2
x = INTG (0.4mm + 2.3)
z = (yyyy)
INTG = Integer portion.
NPV = net present value of a discounted cash flow.
CF
j
= cash flow at period j.
n = number of cash flows
CF
j
= cash flow at period j.
IRR = Internal Rate of Return
CF
0
CF
1
1 i+()
1
------------------
CF
2
1 i+()
2
------------------
CF
n
1 i+()
n
------------------++++
CF
j
j
1=
k
11IRR+()
n
j
IRR
---------------------------------------
1 IRR+()
nq
qj<
⋅⋅ CF
0
+
188 Appendix E: Formulas Used
30/360 Day Basis
DAYS = f(DT
2
) – f(DT
1
)
f(DT) = 360 (yyyy) + 30mm + z
for f(DT
1
)
if dd
1
= 31 then z = 30
if dd
1
31 then z = dd
1
for f(DT
2
)
if dd
2
= 31 and dd
1
= 30 or 31 then z = 30
if dd
2
= 31 and dd
1
< 30 then z = dd
2
if dd
2
< 31 then z = dd
2
Bonds
Reference:
Spence, Graudenz, and Lynch, Standard Securities Calculation Methods, Securi-
ties Industry Association, New York, 1973.
For semiannual coupon with 6 months or less to maturity:
PRICE =
DIM = days between issue date and maturity date.
DSM = days between settlement date and maturity date.
DCS = days between beginning of current coupon period
and settlement date.
E = number of days in coupon period where settlement
occurs.
DSC = EDCS = days from settlement date to next 6-
month coupon date.
N = number of semiannual coupons payable between
settlement date and maturity date.
CPN = annual coupon rate (as a percentage).
YIELD = annual yield (as a percentage).
PRICE = dollar price per $100 par value.
RDV = redemption value.
100 RDV
CPN
2
------------+


100
DSM
E
-------------
YIELD
2
------------------
×


+
----------------------------------------------------------
DCS
E
------------
CPN
2
------------
×
Appendix E: Formulas Used 189
For semiannual coupon with more than 6 months to maturity:
PRICE =
Depreciation
Straight-Line Depreciation
Keyboard function:
DPN
j
= for j = 1, 2, …, L
Program for partial first year:
DPN
1
=
DPN
j
= for j = 2, 3, …, L
DPN
L + 1
= RDV
L
L = asset’s useful life expectancy.
SBV = starting book value.
SAL = salvage value.
FA C T = declining-balance factor expressed as a percent-
age.
j = period number.
DPN
j
= depreciation expense during period j.
RDV
j
= remaining depreciable value at end of period j
= RDV
j–1
DPN
j
where RDV
0
= SBVSAL
RBV
j
= remaining book value = RBV
j–1
DPN
j
where
RBV
0
= SBV
Y
1
= number of months in partial first year.
RDV
1
YIELD
200
------------------+


N 1
DSC
E
------------+
----------------------------------------------------------
CPN
2
------------
1
YIELD
200
------------------+


K 1
DSC
E
------------+
----------------------------------------------------------
K 1=
N
CPN
2
------------
DCS
E
------------
×+
SBV SAL
L
---------------------------
SBV SAL
L
---------------------------
Y
1
12
------
SBV SAL
L
---------------------------
190 Appendix E: Formulas Used
Sum-of-the-Years-Digits Depreciation
SOYD
k
=
where W = integer part of k
F = fractional part of k.
(i.e., for k = 12.25 years, W = 12 and F = 0.25).
Keyboard function:
DPN
j
=
Program for partial year:
DPN
1
=
DPN
j
= for j 1
where LADJ =
Declining-Balance Depreciation
Keyboard function:
DPN
j
= for j = 1, 2, …, L
Program for partial first year:
DPN
1
=
DPN
j
= for j 1
Modified Internal Rate of Return
n = number of compounding periods.
NFV
P
= Net future value of the positive cash flows.
NPV
N
= Net present value of the negative cash flows.
W 1+()W 2F+()
2
------------------------------------------
Lj 1+()
SOYD
L
-------------------------
SBV SAL()
L
SOYD
----------------


Y
1
12
------


SBV SAL()⋅⋅
LADJ j 2+
SOYD
LADJ
--------------------------------


SBV D
1
SAL()
L
Y
1
12
------


RBV
j 1
FACT
100L
---------------
SBV
FACT
100L
---------------
Y
1
12
------
⋅⋅
RBV
j 1
FACT
100L
---------------
Appendix E: Formulas Used 191
MIRR =
Advance Payments
PMT =
Interest Rate Conversions
Finite Compounding
EFF =
Continuous Compounding
EFF =
Statistics
Mean
A = number of payments made in advance.
C = number of compounding periods per year.
EFF = the effective annual interest rate as a decimal.
NOM = the nominal annual interest rate as a decimal.
100
NFV
P
NPV
N
---------------


1
n
---
1
PV FV 1 i+()
n
11i+()
nA()
i
----------------------------------------- A+
---------------------------------------------------------
1
NOM
C
--------------+


C
1
e
NOM
1()
x
x
n
---------=
y
y
n
---------=
192 Appendix E: Formulas Used
Weighted Mean
Linear Estimation
n = number of data pairs
where B =
Standard Deviation
Factorial
0! = 1
For n > 1 where n is an integer:
x
w
wx
w
--------------=
y
ˆ
ABx+=
x
ˆ
yA
B
------------=
xy
x
y
n
------------------------
x
2
x
()
2
2
-----------------
-------------------------------------------
AyBx=
r
xy
x
y
n
------------------------
x
2
x
()
2
n
----------------- y
2
y
()
2
n
-----------------
-------------------------------------------------------------------------------------------=
s
x
nx
2
x
()
2
nn 1()
---------------------------------------=
s
y
ny
2
y
()
2
nn 1()
---------------------------------------=
Appendix E: Formulas Used 193
n! =
The Rent or Buy Decision
Market Value = PRICE(1 + I)
n
where:
Net Cash Proceeds on Resale = Market Value – Mortgage Balance – Commis-
sion
The interest rate is obtained by solving the financial (compound interest) equa-
tion for i using:
Annual interest rate = 12 × i
I = appreciation per year (as decimal)
n = number of years
n = number of years house is owned
PV = down payment + closing costs
PMT = mortgage payment + taxes + maintenance – rent –
(% tax) (interest + taxes)
FV = net cash proceeds on resale
i
i 1=
n
195
Appendix F
Battery, Warranty, and Service
Information
Battery
The HP 12C Platinum is shipped with one 3 Volt CR2023 Lithium battery. Bat-
tery life depends on how the calculator is used. If the calculator is being used to
perform operations other than running programs, it uses much less power.
Low-Power Indication
A battery symbol ( ) shown in the upper-left corner of the display when the
calculator is on signifies that the available battery power is running low. When
the battery symbol begins flashing, replace the battery as soon as possible to
avoid losing data.
Use only a fresh battery. Do not use rechargeable batteries.
Installing a New Battery
The contents of the calculators Continuous Memory are preserved for a short
time while the battery is out of the calculator (provided that you turn off the cal-
culator before removing the battery). This allows you ample time to replace the
battery without losing data or programs. If the battery is left out of the calculator
for an extended period, the contents of Continuous Memory may be lost.
Warning
There is the danger of explosion if the battery is incor-
rectly replaced. Replace only with the same or equiva-
lent type recommended by the manufacturer. Dispose
of used batteries according to the manufacturers
instructions. Do not mutilate, puncture, or dispose of
batteries in fire. The batteries can burst or explode,
releasing hazardous chemicals. Replacement battery
is a Lithium 3V Coin Type CR2032.
196 Appendix F: Battery, Warranty, and Service Information
To install a new battery, use the following procedure:
1. With the calculator turned off, slide the battery cover off.
2. Remove the old battery.
3. Insert a new battery, with positive polarity facing outward.
4. Replace the battery cover.
Note: Be careful not to press any keys while the battery is out of the calculator. If
you do so, the contents of Continuous Memory may be lost and keyboard control
may be lost (that is, the calculator may not respond to keystrokes).
5. Replace the battery compartment cover and press ; to turn on the
power. If for any reason Continuous Memory has been reset (that is, if its
contents have been lost), the display will show Pr Error. Pressing any key
will clear this message.
Verifying Proper Operation (Self-Tests)
If it appears that the calculator will not turn on or otherwise is not operating
properly, use one of the following procedures.
Appendix F: Battery, Warranty, and Service Information 197
For a calculator that does not respond to keystrokes:
1. Insert a thin, pointed object all the way into the reset hole near the battery
compartment and then remove it.
1. The display will show Pr Error. Pressing any key will clear this message
from the display.
2. If the calculator still does not respond to keystrokes, remove and re-insert
the battery. Make sure that the battery is properly positioned in the battery
compartment.
3. If the calculator does not turn on, install a fresh battery. If there is still no
response, the calculator requires service.
For a calculator that does respond to keystrokes:
1. With the calculator off, hold down the ; key and press §.
2. Release the ; key, then release the § key. This initiates a complete test
of the calculators electronic circuitry. If everything is working correctly,
within about 15 seconds (during which the word running flashes) the
display should show –8,8,8,8,8,8,8,8,8,8, and all of the status indicators
should turn on.
1
If the display shows Error 9, goes blank, or otherwise
does not show the proper result, the calculator requires service.
2
1.
The status indicators turned on at the end of this test include some that normally are not
displayed on the
HP 12C Platinum.
2.
If the calculator displays Error 9 as a result of the ;/§ test or the ;/+ test but you
wish to continue using your calculator, you should reset Continuous Memory as described on
page 70.
198 Appendix F: Battery, Warranty, and Service Information
Note: Tests of the calculators electronics are also performed if the = key
or the z key is held down when ; is released.
3
These tests are
included in the calculator to be used in verifying that it. is operating
properly during manufacturing and service.
If you had suspected that the calculator was not working properly but the proper
display was obtained in step 2, it is likely that you made an error in operating the
calculator. We suggest you reread the section in this handbook applicable to your
calculation – including, if appropriate, appendix A. If you still experience diffi-
culty, write or telephone Hewlett-Packard at an address or phone number listed
under Service (page 200).
Warranty
HP 12C Platinum Financial Calculator; Warranty period: 12 months
1. HP warrants to you, the end-user customer, that HP hardware, accessories
and supplies will be free from defects in materials and workmanship after
the date of purchase, for the period specified above. If HP receives notice
of such defects during the warranty period, HP will, at its option, either
repair or replace products which prove to be defective. Replacement
products may be either new or like-new.
2. HP warrants to you that HP software will not fail to execute its
programming instructions after the date of purchase, for the period
specified above, due to defects in material and workmanship when
properly installed and used. If HP receives notice of such defects during
the warranty period, HP will replace software media which does not
execute its programming instructions due to such defects.
3. HP does not warrant that the operation of HP products will be
uninterrupted or error free. If HP is unable, within a reasonable time, to
repair or replace any product to a condition as warranted, you will be
3.
The ;/= combination initiates a test that is similar to that described above, but continues
indefinitely. The test can be terminated by pressing any key, which will halt the test within 25
seconds. The ;/z combination initiates a test of the keyboard and the display. When the
; key is released, certain segments in the display will be lit. To run the test, the keys are
pressed in order from left to right along each row, from the top row to the bottom row. As
each key is pressed, different segments in the display are lit. If the calculator is operating
properly and all the keys are pressed in the proper order, the calculator will display 12 after
the last key is pressed. (The
\ key should be pressed both with the third-row keys and
with the fourth-row keys.) If the calculator is not working properly, or if a key is pressed out
of order, the calculator will display Error 9. Note that if this error display results from an
incorrect key being pressed, this does not indicate that your calculator requires service. This
test can be terminated by pressing any key out of order (which will, of course, result in the
Error 9 display). Both the Error 9 display and the 12 display can be cleared by pressing any
key.
Appendix F: Battery, Warranty, and Service Information 199
entitled to a refund of the purchase price upon prompt return of the
product.
4. HP products may contain remanufactured parts equivalent to new in
performance or may have been subject to incidental use.
5. Warranty does not apply to defects resulting from (a) improper or
inadequate maintenance or calibration, (b) software, interfacing, parts or
supplies not supplied by HP, (c) unauthorized modification or misuse, (d)
operation outside of the published environmental specifications for the
product, or (e) improper site preparation or maintenance.
6. HP MAKES NO OTHER EXPRESS WARRANTY OR CONDITION
WHETHER WRITTEN OR ORAL. TO THE EXTENT ALLOWED BY
LOCAL LAW, ANY IMPLIED WARRANTY OR CONDITION OF
MERCHANTABILITY, SATISFACTORY QUALITY, OR FITNESS FOR
A PARTICULAR PURPOSE IS LIMITED TO THE DURATION OF THE
EXPRESS WARRANTY SET FORTH ABOVE. Some countries, states or
provinces do not allow limitations on the duration of an implied warranty,
so the above limitation or exclusion might not apply to you. This warranty
gives you specific legal rights and you might also have other rights that
vary from country to country, state to state, or province to province.
7. TO THE EXTENT ALLOWED BY LOCAL LAW, THE REMEDIES IN
THIS WARRANTY STATEMENT ARE YOUR SOLE AND
EXCLUSIVE REMEDIES. EXCEPT AS INDICATED ABOVE, IN NO
EVENT WILL HP OR ITS SUPPLIERS BE LIABLE FOR LOSS OF
DATA OR FOR DIRECT, SPECIAL, INCIDENTAL,
CONSEQUENTIAL (INCLUDING LOST PROFIT OR DATA), OR
OTHER DAMAGE, WHETHER BASED IN CONTRACT, TORT, OR
OTHERWISE. Some countries, States or provinces do not allow the
exclusion or limitation of incidental or consequential damages, so the
above limitation or exclusion may not apply to you.
FOR CONSUMER TRANSACTIONS IN AUSTRALIA AND NEW
ZEALAND: THE WARRANTY TERMS CONTAINED IN THIS STATE-
MENT, EXCEPT TO THE EXTENT LAWFULLY PERMITTED, DO NOT
EXCLUDE, RESTRICT OR MODIFY AND ARE IN ADDITION TO THE
MANDATORY STATUTORY RIGHTS APPLICABLE TO THE SALE OF
THIS PRODUCT TO YOU.
200 Appendix F: Battery, Warranty, and Service Information
Service
Argentina 0-810-555-5520
Austria +43-1-3602771203
Belgium +32-2-7126219
Brazil Sao Paulo 3747-7799;
elsewhere 0-800-157751
Canada +1 905 206 4663
Central America & Caribbean 1-800-711-2884
Chile 800-360999
Columbia 9-800-114726
Costa Rica 0-800-011-0524
Czech Republic +420-5-41422523
Denmark +45-8-2332844
Eastern Europe countries +420-5-41422523
Finland +35-89640009
France +33-1-49939006
Germany +49-69-95307103
Greece +420-5-41422523
Guatemala 1-800-999-5105
Holland +31-2-06545301
Israel +420-5-41422523
Italy +39-0422-303069
Luxembourg +32-2-7126219
Mexico Mexico City 5258-9922;
elsewhere 01-800-472-6684
Norway +47-63849309
Peru 0-800-10111
Poland +48-12-4270266
Portugal +351-213-180020
Puerto Rico 1-877-232-0589
Spain +34-917-820111
Sweden +46-851992065
Switzerland +41-1-4395358 (German)
+41-22-8278780 (French)
+39-0422-303069 (Italian)
Turkey +420-5-41422523
UK +44-207-4580161
USA +1 208 323 2551
Venezuela 0800-4746-8368
Appendix F: Battery, Warranty, and Service Information 201
Potential For Radio/Television Interference (for
U.S.A. Only)
The HP 12C Platinum generates and uses radio frequency energy and if not
installed and used properly, that is, in strict accordance with the manufacturers
instructions, may cause interference to radio and television reception. It has been
type tested and found to comply with the limits for a Class B computing device
in accordance with the specifications in Subpart J of Part 15 of FCC Rules,
which are designed to provide reasonable protection against such interference in
a residential installation. However, there is no guarantee that interference will
not occur in a particular installation. If your HP 12C Platinum does cause inter-
ference to radio or television reception, which can be determined by turning the
calculator off and on, you are encouraged to try to correct the interference by one
or more of the following measures:
z Reorient the receiving antenna.
z Relocate the calculator with respect to the receiver.
z Move the calculator away from the receiver.
If necessary, you should consult your dealer or an experienced radio/television
technician for additional suggestions. You may find the following booklet pre-
pared by the Federal Communications Commission helpful: How to Identify and
Resolve Radio TV Interference Problems. This booklet is available from the U.S.
Government Printing Office, Washington, D.C. 20402, Stock No.
004-000-00345-4.
Temperature Specifications
z Operating: 0° to 55° C (32° to 131° F)
z Storage: –40° to 65° C (–40° to 149° F)
Noise Declaration
In the operator position under normal operation (per ISO 7779): LpA < 70dB.
202 Appendix F: Battery, Warranty, and Service Information
Regulation applying to The Netherlands
A battery is delivered with this product.
When empty, do not throw it away, but col-
lect it as small chemical waste.
Bij dit produkt zijn betterijen geleverd.Wan-
neer deze leeg zijn, moet u ze niet weggooien
maar inleverenals KCA.
203
Appendix G
United Kingdom Calculations
The calculations for most financial problems in the United Kingdom are identi-
cal to the calculations for those problems in the United States – which are
described earlier in this handbook. Certain problems, however, require different
calculation methods in the United Kingdom than in the United States, even
though the terminology describing the problems may be similar. Therefore, it is
recommended that you ascertain the usual practice in the United Kingdom for
the financial problem you are solving.
The remainder of this appendix describes three types of financial calculations for
which the conventional practice differs significantly between the United King-
dom and the United States.
Mortgages
The amount of the repayments on home loans and mortgages offered by banks in
the United Kingdom can usually be calculated as described under Calculating the
Payment Amount, page 48. Building Societies in the United Kingdom, however,
calculate the amount of these repayments differently. In general, the repayment
amount of a Building Society mortgage is calculated as follows: first, the annual
repayment amount is calculated using the annual interest rate; second, the peri-
odic repayment amount is calculated by dividing the annual repayment amount
by the number of repayment periods in one year.
Furthermore, the calculations used by Building Societies are rounded; therefore,
to match their scale repayment figures you would have to round your calcula-
tions accordingly.
Annual Percentage Rate (APR) Calculations
In the United Kingdom, the calculation of the Annual Percentage Rate of Charge
(APR) in accordance with the United Kingdom Consumer Credit Act (1974) dif-
fers from the calculation of the APR in the United States. Unlike the practice in
the United States, where the APR can be calculated by multiplying the periodic
interest rate by the number of periods per year, in the United Kingdom the APR
is calculated by converting the periodic interest rate to the “effective annual
rate,” then truncating the result to one decimal place. With the periodic interest
rate in the display and in the i register, the effective annual rate can be calculated
by keying in the number of compounding periods per year, pressing w, then
proceeding with step 4 of the procedure given on page 156 for converting a nom-
inal rate to an effective rate.
204 Appendix G: United Kingdom Calculations
Bond Calculations
Solutions for the price and yield to maturity of United Kingdom bonds are not
included in this handbook. Actual practice differs according to the type of bond;
variations such as cumulative and ex-dividend pricing, simple or compound
interest discounting, etc., may be encountered.
Application Notes covering such situations may be available in the United King-
dom; check with your local authorized Hewlett-Packard dealer.
205
Function Key Index
General
; Power on /off key
(page 16).
f
Shift key. Selects alter-
nate function in gold above
the function keys
(page 16). Also used in
display formatting
(page 71).
g Shift key. Selects alter-
nate function in blue on the
slanted face of the function
keys (page 16).
CLEARX after f, g,
?, :or i, cancels
that key (page 18).
fCLEARX also dis-
plays mantissa of number
in the displayed X-register
(page 73).
Digit Entry
\ Enters a copy of num-
ber in displayed X-register
into Y-register. Used to
separate numbers (pages
19 and 167).
Þ Changes sign of num-
ber or exponent of 10 in
X-register (page 17).
Æ Enter exponent. After
pressing, next numbers
keyed in are exponents of
10 (page 18).
0 9 digits. Used for
keying in numbers (page
19) and display formatting
(page 70).
. Decimal point (page
17). Also used for dis-
play formatting (page
72).
OClears contents of
displayed X-register to
zero (page 18).
Arithmetic
+-§z} Arith-
metic operators (page
19).
Storage Registers
? Store. Followed by
number key, decimal
point and number key,
or top row financial key,
stores displayed num-
ber in storage register
specified (page 24).
Also used to perform
storage register arith-
metic (page 25).
:Recall. Followed by
number key, decimal
point and number key,
or top-row financial key,
recalls value from stor-
age register specified
into the displayed X-reg-
ister (page 24).
CLEAR H Clears con-
tents of stack (X,Y,Z and
T), all storage registers,
statistical registers, and
financial registers (page
25). Leaves program
memory untouched; not
programmable.
Percentage
b Computes x% of y and
retains the y-value in the
Y-register (page 27).
à Computes percent of
change between number in
Y-register and number in
displayed X-register (page
28).
Z Computes percent that
x is of number in Y-register
(page 29).
Calendar
Ô Sets date format to
day-month-year (page 31);
not programmable.
Õ Sets date format to
month-day-year (page 30);
not programmable.
D Changes a date in the
Y-register by the number of
days in the X-register and
displays day of week (page
31).
Ò Computes the number
of days between two dates
in the Y- and X-registers
(page 32).
Financial
CLEARG Clears con-
tents of financial registers
(page 34).
× Sets payment mode to
Begin for compound inter-
est calculations involving
payments (page 39).
206 Function Key Index
 Sets payment
mode to End for com-
pound interest calcula-
tions involving
payments (page 39).
Ï Calculates simple
interest (page 35).
w Stores or computes
number of periods in
financial problem (page
34).
A Multiplies a number
in displayed X-register
by 12 and stores the
resulting value in the
n-register (page 41).
¼ Stores or computes
interest rate per com-
pounding period (page
34).
C Divides number in
displayed X-register by
12 and stores the result-
ing value in the i-register
(page41).
$ Stores or computes
the present value (that
is, the initial cash flow)
of a financial problem
(page 34).
P Stores or computes
payment amount (page
34).
M Stores or computes
future value (final cash
flow) of a financial prob-
lem (page 34).
! Amortizes x num-
ber of periods using val-
ues stored in PMT, i, PV,
and the display.
Updates values in PV
and n (page 54).
l Calculates the net
present value of up to
30 uneven cash flows
and initial investment
using values stored with
J, K, and a
(page 59).
L Calculates the
internal rate of return
(yield) for up to 30
uneven cash flows and
initial investment using
values stored with J,
K, and a (page 63).
J Initial cash flow.
Stores contents of dis-
played X-register in R
0
,
initializes n to zero, sets
N
0
to 1. Used at the
beginning of a dis-
counted cash flow prob-
lem (page 59).
K Cash flow j. Stores
the contents of X-
register in R
j
, incre-
ments n by 1, and sets
N
j
to 1. Used for all cash
flows except the initial
cash flow in a dis-
counted cash flow prob-
lem (page 59).
V Calculates depreci-
ation using straight-line
method. (page 68).
E Calculates bond
price, given desired
yield to maturity (page
67).
S Calculates yield to
maturity, given bond
price (page 68).
a Stores the number
(from 1 to 99) of times
each cash flow occurs
as N
j
. Assumes 1 unless
otherwise specified
(page 61).
Ý Calculates depreci-
ation using
sum-of-the-years-digits
method (page 68).
#Calculates deprecia-
tion using declining-bal-
ance method (page 68).
Statistics
CLEAR² Clears statis-
tical storage registers
R
1
through R
6
and stack
registers (page 76).
_ Accumulates statis-
tics using numbers from
X- and Y-registers in
storage registers R
1
through R
6
(page 76).
^ Cancels effect of
numbers from X- and
Y-registers in storage
registers R
1
through R
6
(page 77).
Ö Computes mean
(average) of x-values
and y-values using
accumulated statistics
(page 77).
h Computes weighted
average of y-(item) and
x-(weight) values using
accumulated statistics
(page 81).
v Computes sample
standard deviations of x-
and y-values using
accumulated statistics
(page 78).
Function Key Index 207
R Linear estimate
(X-register), correlation
coefficient (Y-register).
Fits a line to a set of (x,y)
data pairs entered using
_, then extrapolates
this line to estimate a
y-value for a given
x-value. Also computes
strength of linear
relationship (r) among
that set of (x, y) data
pairs (page 79).
Q Linear estimate
(X-register), correlation
coefficient (Y-register).
Fits a line to a set of (x,
y) data pairs entered
using _, then extra-
polates this line to esti-
mate an x-value for a
given y-value. Also com-
putes strength of linear
relationship (r) among
that set of (x,y) data
pairs (page 79).
Modes
] sets calculator to
RPN mode (page 19).
[ sets calculator to
algebraic (ALG) mode
(page 19).
Mathematics
r Computes square root
of number in displayed
X-register (page 82).
q Raises number in
Y-register to power of num-
ber in X-register (page 82).
y Computes reciprocal of
number in displayed X-reg-
ister (page 82).
e Computes factorial
[n·(n–1)... 3·2·1] of number
in displayed X-register
(page 82).
> Natural antilogarithm.
Raises e (approximately
2.718281828) to power of
number in displayed X-reg-
ister (page 82).
° Computes natural log-
arithm (base e) of number
in displayed X-register
(page 82).
Computes square of
the number displayed in
the X-register (page 82).
Number Alteration
B Rounds mantissa of
10-digit number in X-regis-
ter to match the display
(page 82).
Ñ Leaves only the inte-
ger portion of number in
displayed X-register by
truncating fractional portion
(page 83).
T Leaves only the frac-
tional portion of number in
displayed X-register by
truncating integer portion
(page 83).
Stack Rearrangement
~ Exchanges contents
of X- and Y-registers of
stack (pages 74 and 168).
d RolIs down contents of
stack for viewing in dis-
played X-register (page
168).
F Recalls number dis-
played before the previous
operation back into the dis-
played X-register (pages
74 and 172).
208
Programming Key Index
s Program/Run. Toggles into and out of Program mode. Automatically sets
program to line 000 when returning to Run mode (page 86).
N Memory map. Describes the current allocation of memory; the number of
lines allotted to program memory and the number of available data registers
(page 93).
Program Mode Run Mode
In Program mode,
function keys are
recorded in program
memory. Display
shows program
memory line number
and the keycode
(keyboard row and
location in row) of
the function key.
In Run mode, function keys may be executed
as part of a recorded program or individually by
pressing from the keyboard.
Active Keys:
In Program mode only
the following keys are
active; they cannot be
recorded in program
memory.
CLEARÎ
Clear program. Clears
program memory to all
i000 instructions
and resets calculator so
operations begin at line
000 of program mem-
ory. Resets N to
P008 r-20 (page 86)
Pressed from
keyboard:
CLEARÎ
Resets calculator (in
Run mode) so opera-
tions begin at line 000
of program memory.
Does not erase pro-
gram memory.
Executed as a
recorded program
instruction
Programming Key Index 209
Program Mode Run Mode
Active Keys:
i Go to. Followed by
a decimal point and a
three-digit number,
positions calculator to
that line in program
memory. No instruc-
tions are executed
(page 93)
Ê Single step. Dis-
plays line number and
contents of next pro-
gram memory line. If
held down, displays line
number and contents of
all program memory
lines, one at a time
(page 90).
Ü Back step. Dis-
plays line number and
contents of previous
program memory line.
When back stepped
from line 000, goes to
end of program memory
as defined by gN. If
held down, displays line
number and contents of
all program memory
lines, one at a time
(page 90).
Pressed from
keyboard:
t Run/Stop. Begins
execution of a stored
program. Stops execu-
tion if program is run-
ning (page 87).
i Go to. Followed by
a three-digit number,
positions calculator to
that line in program
memory. No instruc-
tions are executed
(page 101).
Ê Single step. Dis-
plays line number and
keycode of current pro-
gram memory line when
pressed; executes
instruction, displays
result, and moves to
next line when released
(page 94).
Ü Back step. Dis-
plays line number and
keycode of previous
program memory line
when pressed; displays
original contents of
X-register when
released. No
instructions are exe-
cuted (page 95).
Any key. Pressing any
key on the keyboard
stops execution of a
program (page 100)
Executed as a recorded
program instruction:
t Run/Stop. Stops
program execution
(page 98).
i Go to. Followed by
a three-digit number,
causes calculator to
branch to the specified
line number next, and
resumes program exe-
cution from there (page
101).
u Pause. Stops pro-
gram execution for
about 1 second and dis-
plays contents of X-reg-
ister, then resumes
program execution
(page 95).
om Conditional.
o tests number in
X-register against that
in Y-register. m tests
number in X-register
against zero. If true,
calculator continues
execution at next pro-
gram memory line. If
false, calculator skips
next line before resum-
ing execution (page
104)
211
Subject Index
A
Adding instructions 111115
Advance payments 148, 152
Algebraic mode
19, 175
! 12, 55, 168
Amortization 40, 5457, 186
Annual interest rate
41
Annual Percentage Rate 5354, 122124, 203
Annuities 38
Annuities, deferred
131133
Annuity due 3940
Appreciation 40
APR, See Annual Percentage Rate
Arithmetic calculations with constants
75, 173
Arithmetic calculations, chain 2023
Arithmetic calculations, simple
19
Arithmetic operations and the stack 169
Arithmetic, storage register 25
Asterisk in display
195
Average See Mean
B
Backstep 90
Balloon payments
42, 43
Battery
195196
Battery power, low
11, 16, 195
Battery, installing
195196
× 39
BEGIN status indicator
39
Bonds 6768, 159163, 188189, 204
Bonds, 30/360 day basis
159161
Bonds, annual coupon 161
Bonds, corporate 67
Bonds, municipal
67
Bonds, state and local government 67
Bonds, U.S. Treasury 67
Branching
101109, 113
212 Index
Branching, adding instructions by 113115
Branching, conditional 104106
Branching,simple 101
Ü 90
Buying versus Renting 127
C
C status indicator 53
Calendar functions 3033, 187188
Calendar functions and the stack 171
J 61
Cash flow diagram 3640
Cash flow sign convention 35, 38
K 60, 62, 64
Cash flows, changing 66
Cash flows, reviewing 64
Cash flows, storing for I and L
59, 66
Chain calculations 2023, 172173, 176
Þ 17, 20, 35, 59
O 18, 29
Clearing display 18
Clearing financial registers 18
Clearing operations
17, 18
Clearing prefix keys 17
Clearing program memory
18, 87
Clearing statistics registers 18, 76
Clearing storage registers 18, 25, 70
Clearing X-register
18
Compound growth 41
Compound interest
4154, 185
Compound interest calculation
11
Compounding periods 36, 41
Conditional branching 104106
Conditional test instructions
105
Constants, arithmetic calculations with
75, 173
Continuous compounding 158, 191
Continuous effective rate
158
Continuous memory
70
Continuous memory, resetting of 35, 39, 70, 72, 91
Q 168
R 168
Index 213
D
D 3033
D.MY status indicator 31
Data storage registers
2326
Date format 30, 70
Dates, days between 32
Dates, future or past
31
Days, between dates 32
# 69, 168
Decimal places, rounding
71
Decimal point, changing 17
Declining-balance depreciation 137
Deferred annuities
131133
Depreciation 68, 134145, 189190
Depreciation, excess 145
Depreciation, partial year
134145
Depreciation, sum-of-the-years -digits 139
Depreciation, with crossover 141145
Depreciation,declining-balance
137
Digit entry, recovering from errors in 75
Digit entry, termination of 20, 167
Discounted cashflow analysis
58
Display 70
Display format, mantissa 73
Display format, standard
71
Display formats, number 71
Display, scientific notation
72
Displaying numbers 34
Displays, special
73
Ò 52, 168
E
Editing a program 110
Effective interest rate, converting
157
Entry errors 75
Error conditions 74
Error, Pr
74
Errors 74
Errors, in digit entry 75
Excess depreciation
145
Æ 18
214 Index
Exponent 18, 84
Exponential 82
F
Factorial 82
Financial registers 34
Financial registers, clearing 34
Fractional
83
Future value 38
Future value, calculating 49
FV
38
G–K
i 91
Indicators, status
70
Instructions in program lines 89
¼ 12
Ï 168
Interest rate, annual 45
Interest rate, periodic
45
Interest, simple 35
Internal rate of return 58
Internal rate of return, calculating
63
Internal rate of return, modified 145
Interrupting a program
95
IRR
58, 145
L 12
Keyboard
16
L
LAST X register 70
Leasing 148
Linear estimation
79
Logarithm 82
Looping 101
Low-power indicator
16
F 74
Index 215
M
Mantissa 18, 73
Mantissa Display Format 73
Mean
77
Ö 168
Mean, weighted 81
memory
23
Memory, program 91
Modes
alegebraic
19
RPN 19
Modified internal rate of return 145
Mortgage, price of
124
Mortgage, yield of 125
Multiple programs 117
N
Negative numbers 17, 175
Net amount
27
Net present value 58
Net present value, calculating 59
Nominal interest rate, converting
156
Nominal rate 158
NPV 58
Number display formats
71
Numbers, keying in
17
Numbers, large
18
Numbers, negative
17
Numbers, recalling
24
Numbers, storing
24
O
Odd-period calculations 51
Odd-period mode 37
One-number functions
82
One-variable statistics 76
Overflow 73
216 Index
P
Partial-year depreciation 134
Payment 38, 152
Payment amount, calculating
48
Payment mode 38
Payments, advance 148, 152
Payments, number of
41
Percent difference 28, 177
Percent of total 29, 177
Percentages
27, 176
PMT 38
Populations 79
Power function
84, 178
Pr error 74
Prefix key 16
Present value
38
Present value, calculating 46
PRGM status indicator 86, 87
Program branching
101
Program editing 110
Program lines, displaying 90
Program looping
101
Program memory 88, 91
Program mode 86
Program, creating
86
Program, interrupting 95
Program, running
87, 119
Program, running one line at a time 91
Program, stopping
95, 98
Program, storing
117
Programming 86
Programs, multiple
117
u 95
PV
38
R
Reciprocal 82
registers 23
Registers, financial 34
Registers, statistics
76
Renting versus Buying 127
Index 217
Residual 152
E 168
Round 82
B 82
Rounding 71
RPN mode 19, 20, 166
Running message
12, 63
S
v 168
Samples
79
Savings 156
Scientific notation 72
scientific notation
18
Simple branching 101
Simple interest 35
V 168
Ý 168
Square Root 82
Stack
166
Standard deviation 78
Statistics 76
Status indicators
70
? 24
Storage register arithmetic
25
Storage registers, clearing 25
Storing numbers 34
Storing programs
117
Straightline depreciation 134
Sum-of-the-years -digits depreciation
139
T–Z
Two-variable statistics 76
Underflow 73
Weighted mean
81
~ 74
Yield 150, 154
S 12
189

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