HP 12C Platinum manual

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  • Brand: HP
  • Product: Calculator
  • Model/name: 12C Platinum
  • Filetype: PDF
  • Available languages: English

Table of Contents

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File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 1 of 275
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm
hp 12c platinum financial calculator
user's guide
H
Edition 4
HP part number F2232-90001
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Notice
REGISTER YOUR PRODUCT AT: www.register.hp.com
THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN
ARE PROVIDED “AS IS” AND ARE SUBJECT TO CHANGE
WITHOUT NOTICE. HEWLETT-PACKARD COMPANY MAKES
NO WARRANTY OF ANY KIND WITH REGARD TO THIS
MANUAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY, NON-INFRINGEMENT
AND FITNESS FOR A PARTICULAR PURPOSE.
HEWLETT-PACKARD CO. SHALL NOT BE LIABLE FOR ANY
ERRORS OR FOR INCIDENTAL OR CONSEQUENTIAL
DAMAGES IN CONNECTION WITH THE FURNISHING,
PERFORMANCE, OR USE OF THIS MANUAL OR THE
EXAMPLES CONTAINED HEREIN.
© Copyright 1981, 1982, 1999, 2002-2005 Hewlett-Packard
Development Company, L.P. Reproduction, adaptation, or translation
of this manual is prohibited without prior written permission of
Hewlett-Packard Company, except as allowed under the copyright
laws.
Hewlett-Packard Company
4995 Murphy Canyon Rd,
Suite 301
San Diego, CA 92123
Printing History
Edition 4 March 2005
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Introduction
About This Handbook
This hp 12c platinum user's 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) describes how to use the powerful
programming capabilities of the hp 12c platinum.
z Part III (sections 12 through 16) gives 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.
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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, options pricing, and queuing theory.
The solutions handbook is available online at the hp 12c platinum website.
HP would like to thank the following for their contribution:
Gene Wright, Lipscomb University, Nashville, TN, USA
and
Tony Hutchins, Wellington, NZ
Jordi Hidalgo, Barcelona, Spain
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Contents
Introduction.................................................................... 3
About This Handbook.....................................................................3
Financial Calculations in the United Kingdom.....................................4
For More Solutions to Financial Problems...........................................4
Part I: Problem Solving ......................................... 15
Section 1: Getting Started ................................................. 16
Power On and Off........................................................................16
Low-Power Indication..............................................................16
Adjusting the Display Contrast.................................................16
The Keyboard ..............................................................................16
Keying in Numbers ................................................................17
Digit Separators ....................................................................17
Negative Numbers ................................................................17
Keying in Large Numbers .......................................................18
Backspacing .........................................................................18
The CLEAR Keys ....................................................................19
Undo Operation....................................................................20
The RPN and ALG Keys ..........................................................20
Simple Arithmetic Calculations in RPN Mode ...................................21
Simple Arithmetic Calculations in ALG Mode ...................................22
Chain Calculations in RPN Mode...................................................23
Chain Calculations in ALG Mode ...................................................26
Parentheses Calculations ...............................................................26
Storage Registers..........................................................................27
Storing and Recalling Numbers...............................................27
Clearing Storage Registers......................................................29
Storage Register Arithmetic .....................................................29
Section 2: Percentage and Calendar Functions .................... 31
Percentage Functions.....................................................................31
Percentages in RPN Mode ......................................................31
Percentages in ALG Mode ......................................................32
Net Amount in RPN Mode......................................................33
Net Amount in ALG Mode ......................................................33
Percent Difference..................................................................34
Percent of Total in RPN Mode..................................................35
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Percent of Total in ALG Mode ................................................. 36
Calendar Functions...................................................................... 37
Date Format ......................................................................... 37
Future or Past Dates............................................................... 38
Number of Days Between Dates ............................................. 40
Section 3: Basic Financial Functions ....................................41
The Financial Registers ................................................................. 41
Storing Numbers into the Financial Registers ............................ 41
Displaying Numbers in the Financial Registers .......................... 41
Clearing the Financial Registers .............................................. 42
Simple Interest Calculations........................................................... 42
Financial Calculations and the Cash Flow Diagram.......................... 44
The Cash Flow Sign Convention.............................................. 46
The Payment Mode ............................................................... 46
Generalized Cash Flow Diagrams........................................... 47
Compound Interest Calculations..................................................... 49
Specifying the Number of Compounding Periods and the Periodic
Interest Rate ......................................................................... 49
Calculating the Number of Payments or Compounding Periods ... 49
Calculating the Periodic and Annual Interest Rates..................... 55
Calculating the Present Value ................................................. 56
Calculating the Payment Amount............................................. 58
Calculating the Future Value................................................... 60
Odd-Period Calculations ........................................................ 63
Amortization ............................................................................... 69
Section 4: Additional Financial Functions.............................72
Discounted Cash Flow Analysis: NPV and IRR ................................. 72
Calculating Net Present Value (NPV) ....................................... 73
Calculating Internal Rate of Return (IRR) ................................... 78
Reviewing Cash Flow Entries................................................... 79
Changing Cash Flow Entries................................................... 80
Bond Calculations ....................................................................... 82
Bond Price ........................................................................... 82
Bond Yield........................................................................... 83
Depreciation Calculations............................................................. 84
Section 5: Additional Operating Features ............................86
Continuous Memory..................................................................... 86
The Display................................................................................. 87
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Status Indicators ....................................................................87
Number Display Formats ........................................................87
Scientific Notation Display Format ...........................................88
Special Displays ....................................................................90
The Key in RPN Mode..........................................................90
The Key in RPN Mode .........................................................91
Arithmetic Calculations With Constants ....................................91
Recovering From Errors in Digit Entry........................................92
Section 6: Statistics Functions ............................................ 93
Accumulating Statistics..................................................................93
Correcting Accumulated Statistics ...................................................94
Mean .........................................................................................94
Standard Deviation.......................................................................96
Linear Estimation ..........................................................................97
Weighted Mean...........................................................................99
Section 7: Mathematics and Number-Alteration Functions.. 100
One-Number Functions ...............................................................100
The Power Function in RPN Mode.................................................102
The Power Function in ALG Mode.................................................102
Part II: Programming ........................................... 103
Section 8: Programming Basics ........................................ 104
Why Use Programs?...................................................................104
Creating a Program....................................................................104
Running a Program.....................................................................106
Program Memory .......................................................................108
Identifying Instructions in Program Lines ..................................108
Displaying Program Lines......................................................109
The 000 Instruction and Program Line 000 ......................112
Expanding Program Memory ................................................112
Setting the Calculator to a Particular Program Line ...................114
Executing a Program One Line at a Time.......................................114
Interrupting Program Execution.....................................................117
Pausing During Program Execution.........................................117
Stopping Program Execution .................................................122
Section 9: Branching and Looping.....................................125
Simple Branching.......................................................................125
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Looping.................................................................................... 126
Conditional Branching ............................................................... 129
Section 10: Program Editing...............................................139
Changing the Instruction in a Program Line ................................... 139
Adding Instructions at the End of a Program.................................. 140
Adding Instructions within a Program ........................................... 142
Adding Instructions by Replacement ...................................... 142
Adding Instructions by Branching.......................................... 144
Section 11: Multiple Programs............................................149
Storing Another Program ............................................................ 149
Running Another Program........................................................... 153
Part III: Solutions .................................................. 155
Section 12: Real Estate and Lending....................................156
Annual Percentage Rate Calculations With Fees............................. 156
Price of a Mortgage Traded at a Discount or Premium.................... 159
Yield of a Mortgage Traded at a Discount or Premium ................... 161
The Rent or Buy Decision ............................................................ 163
Deferred Annuities ..................................................................... 169
Section 13: Investment Analysis..........................................171
Partial-Year Depreciation............................................................. 171
Straight-Line Depreciation..................................................... 171
Declining-Balance Depreciation .............................................176
Sum-of-the-Years-Digits Depreciation ...................................... 180
Full- and Partial-Year Depreciation with Crossover .......................... 184
Excess Depreciation ................................................................... 191
Modified Internal Rate of Return................................................... 192
Black-Scholes Formula for Valuing European Options...................... 194
Section 14: Leasing ...........................................................202
Advance Payments..................................................................... 202
Solving for Payment............................................................. 202
Solving for Yield ................................................................. 206
Advance Payments With Residual ................................................ 209
Solving for Payment............................................................. 209
Solving for Yield ................................................................. 212
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Section 15: Savings .......................................................... 213
Nominal Rate Converted to Effective Rate......................................213
Effective Rate Converted to Nominal Rate......................................215
Continuous Rate Converted to Effective Rate...................................216
Section 16: Bonds............................................................. 217
30/360 Day Basis Bonds ...........................................................217
Annual Coupon Bonds................................................................222
Appendices ................................................................ 227
Appendix A: RPN and the Stack................................... 228
Getting Numbers Into the Stack: The Key..............................229
Termination of Digit Entry .....................................................230
Stack Lift.............................................................................230
Rearranging Numbers in the Stack ...............................................230
The Key .....................................................................230
The Key.......................................................................230
One-Number Functions and the Stack ...........................................231
Two-Number Functions and the Stack............................................231
Mathematics Functions .........................................................231
Percentage Functions............................................................232
Calendar and Financial Functions.................................................233
The LAST X Register and the Key .........................................234
Chain Calculations in RPN Mode.................................................234
Arithmetic Calculations with Constants ..........................................235
Appendix B: Algebraic Mode (ALG).............................. 237
Simple Arithmetic Calculations in ALG Mode .................................237
Keying in Negative Numbers ( ) .............................................238
Chain Calculations in ALG Mode .................................................238
The Key in ALG Mode .......................................................239
The History Stack in ALG Mode....................................................239
Parentheses Calculations .............................................................240
Percentage Functions...................................................................241
Percent Difference................................................................241
Percent of Total....................................................................242
The Power Function.....................................................................242
Appendix C: More About L...................................... 243
Appendix D: Error Conditions ...................................... 245
Error 0: Mathematics ..................................................................245
Error 1: Storage Register Overflow ...............................................246
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Error 2: Statistics........................................................................ 246
Error 3: IRR............................................................................... 246
Error 4: Memory ....................................................................... 246
Error 5: Compound Interest..........................................................247
Error 6: Storage Registers ............................................................248
Error 7: IRR ................................................................................248
Error 8: Calendar.......................................................................249
Error 9: Service ..........................................................................249
Pr Error .....................................................................................249
Appendix E: Formulas Used......................................... 250
Percentage................................................................................ 250
Interest ..................................................................................... 250
Simple Interest .................................................................... 250
Compound Interest.............................................................. 251
Amortization ............................................................................. 251
Discounted Cash Flow Analysis ....................................................252
Net Present Value ................................................................252
Internal Rate of Return...........................................................252
Calendar...................................................................................252
Actual Day Basis..................................................................252
30/360 Day Basis...............................................................252
Bonds .......................................................................................253
Black-Scholes Formula for Valuing European Options .................... 254
Depreciation ............................................................................. 254
Straight-Line Depreciation......................................................255
Sum-of-the-Years-Digits Depreciation .......................................255
Declining-Balance Depreciation .............................................255
Modified Internal Rate of Return................................................... 256
Advance Payments..................................................................... 256
Interest Rate Conversions ............................................................ 256
Finite Compounding............................................................ 256
Continuous Compounding.................................................... 256
Statistics ....................................................................................257
Mean.................................................................................257
Weighted Mean ..................................................................257
Linear Estimation..................................................................257
Standard Deviation ..............................................................257
Factorial .............................................................................257
The Rent or Buy Decision ............................................................ 258
Appendix F: Battery, Warranty, and Service Information 259
Battery ......................................................................................259
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Low-Power Indication ..................................................................259
Installing a New Battery .......................................................260
Verifying Proper Operation (Self-Tests)...........................................261
Warranty ..................................................................................263
Service .....................................................................................264
Regulatory Information................................................................265
Temperature Specifications ..........................................................266
Noise Declaration ......................................................................266
Disposal of Waste Equipment by Users in Private Household in the
European Union.........................................................................266
Appendix G: United Kingdom Calculations.....................267
Mortgages ................................................................................267
Annual Percentage Rate (APR) Calculations....................................268
Bond Calculations ......................................................................268
Function Key Index.......................................................269
Programming Key Index ...............................................272
Subject Index ..............................................................274
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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 daughter’s
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 PV: 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.*
* If you are not familiar with the use of an hp calculator keyboard, refer to the description on
pages 16 and 17.
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Making Financial Calculations Easy 13
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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
time to produce an answer. (This is typically just a few seconds, but the¼,
!, 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.
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.
g× 500.00 Sets payment mode to Begin.
$ -21,396.61 Amount required to be deposited.*
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 $5,000 insurance policy that pays 5.35%, compounded annually. How
much would it be worth by the time she enters college?
In this example, we need to calculate FV, the future value.
Keystrokes Display
fCLEARG -21,396.61 Clears previous financial data
inside the calculator.
14n 14.00 Stores the number of compounding
periods.
5.35¼ 5.35 Stores the periodic interest rate.
5000Þ$ -5,000.00 Stores the present value of the
policy.
* Don’t be concerned now about the minus sign in the display. That and other details will be
explained in Section 3.
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Keystrokes Display
M 10,371.79 Value of policy in 14 years.
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 – 10,371.79 = 11,024.82). 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 $11,024.82 in the 14 years remaining?
Keystrokes Display
fCLEARG 10,371.79 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.
11024.82M 11,024.82 Stores the future value required.
g 11,024.82 Sets payment mode to End.
P –42.03 Monthly payment required.
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
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.
Keystrokes Display
45ÞP –45.00 Stores payment amount.
¼ 0.43 Periodic interest rate.
:gC 5.13 Annual interest rate.
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 tool, just turn the page.
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Part I
Problem Solving
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Section 1
Getting Started
Power On and Off
To begin using your hp 12c platinum, press the ; key*. Pressing ; again
turns the calculator off. If not manually turned off, the calculator will turn off
automatically 12 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.
Adjusting the Display Contrast
The display’s readability depends on lighting, your viewing angle, and the display
contrast setting. You can adjust the display contrast, by holding down the f key
and pressing + or -.
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:
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.
* Note that the ; key is lower than the other keys to help prevent its being pressed
inadvertently.
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Throughout this handbook, 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 CLEARH function …” or “Pressing
fCLEARH …”).
If you press the f or g prefix key mistakenly, you can cancel it by pressing
fCLEARX. 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 fCLEARX.
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.
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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:
Keystrokes Display
1.7814Æ12 1.7814 12 1,781,400,000,000 entered
in scientific notation.
Numbers entered in scientific notation can be used in calculations just like any
other number.
Backspacing
While you are entering a number, pressing gÚ deletes the last character you
entered. After performing a calculation, pressing gÚ deletes the current
number.
Keystrokes
(RPN mode)
Display
12345gÚgÚ
.63\ 123.63 Correcting removes the 4 and
5. gÚ clears the most recent
digit entered.
5+ 128.63
gÚ 0.00 Clears the calculator line.
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Keystrokes
(ALG mode)
Display
12345gÚgÚ
.63+ 123.63 Correcting removes the 4 and
5. gÚ clears the most recent
digit entered.
5} 128.63 } is also labeled the
\ key.
gÚ 0.00 Clears the calculator line.
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:
Key(s) Clears:
O Display and X-register.
fCLEAR² Statistics registers (R1 through R6), 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.
Note: In ALG mode, it is a good idea to begin calculations by pressing
OO. This will ensure that there are no pending arithmetic calculations
that might interfere with the solution of a new problem. The reason this key is
pressed twice is that pressing it the first time clears the display and X-register
only, allowing you to correct an erroneous entry by keying in a correct
number. The second press of O will clear any pending operations as well.
Pressing the } key is another way to ensure that there are no pending
operations before beginning a new calculation, since the } key will
evaluate any pending expressions.
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Undo Operation
Every time you press O, gÚ, fCLEARH, fCLEAR² or
fCLEARG key to clear data, the status indicator appears in the display.
This means you can press gß to undo the last operation (i.e., to recover the
data.)
Note: the Undo function is only available immediately after data has been
cleared. When the Undo indicator is turned off no operation can be undone.
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, using parentheses if needed.
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: }. Don’t forget to press OO before doing the
calculation.
RPN mode ALG mode
1 \ 2 + 1 + 2 }
You can choose either ALG (Algebraic) or RPN (Reverse Polish
Notation) mode for your calculations. Throughout the manual, most
examples are shown in both modes. The Keystrokes column will
indicate RPN mode or ALG mode where the keystrokes differ. When
the keystrokes are the same, the column is simply titled
“Keystrokes”.
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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.
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:
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.
Notice that after you pressed \, two zeroes appeared following the decimal
point. This is nothing magical: the calculator’s 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 (.)
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Simple Arithmetic Calculations in ALG Mode
In ALG 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 tell the calculator the first number, then
the operation to be performed, and then tell the calculator the second number. The
answer is calculated when the equals key (}) is pressed.
For example, to calculate 21.1 + 23.8, do the following:
Keystrokes
(ALG mode)
Display
OO 0.00 Clears any pending operations.
21.1+ 21.10 Keys in the first number and
prepares to add the second.
23.8 23.8 Keys the second number.
} 44.90 } completes the calculation.
Once a calculation has been completed:
z pressing another digit key starts a new calculation, or
z pressing an operator key continues the calculation.
Keystrokes
(ALG mode)
Display
OO 0.00 Clears any pending operations.
77.35- 77.35
90.89} –13.54 } completes the calculation.
65gr§12} 96.75 New calculation: 12
65 ×
z3.5} 27.64 Calculates 96.75 ÷ 3.5
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. Note that if you have just pressed }, there is no need to
press OO before starting a new calculation – the } key will have completed
any pending operations.
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Chain Calculations in RPN Mode
Whenever the answer has just been calculated and is therefore in the display, you
can perform another operation 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.”
Example: Suppose you’ve written three checks without updating your checkbook,
and you’ve just deposited your paycheck for $1,053 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.
13.7 13.7 Keys in the next number. Since a
calculation has just been performed,
do not press \; the next number
entered (13.7) is automatically
separated from the one previously in
the display (35.38).
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Keystrokes
(RPN mode)
Display
- 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.
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 do the multiplication in the first parentheses, then the
multiplication in the second parentheses, and finally add the results of the two
multiplications:
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Your hp 12c platinum calculates the answer in just the same way in RPN mode:
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.
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 proper
time, just as you would yourself.* 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.
00
.
77
)
6
5
(
)
4
3
( =
+
×
+
25
.
0
)
38
14
(
)
14
27
(
=
+
−
13
.
0
21
16
3
5
=
+
+
* 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 calculator’s operation, you’ll use it more efficiently and
confidently, yielding a better return on the investment in your hp 12c platinum.
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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
360
12
x
750
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:
9
.
1
68
5
.
18
75
456
×
−
This calculation can be written as: 456 – 75 ÷ 18.5 × 68 ÷ 1.9. Watch what
happens in the display as you key it in:
Keystrokes
(ALG mode)
Display
OO 0.00 Clears any pending operations.
456-75z 381.00 Subtracts 75 from 456.
18.5§ 20.59 Divides 381 by 18.5.
68z 1,400.43 Multiplies by 68.
1.9} 737.07 Divides by 1.9 and displays the
result.
Parentheses Calculations
In ALG mode, parentheses can be used in calculations to change the order in
which operations are evaluated. When there are pending open parentheses, the ( )
status indicator will be shown in the display. As open parentheses are closed, the
expression contained within the parentheses is evaluated, from left to right. The
final result of a calculation will be displayed when you press the ³ key, and then
any pending parentheses will be closed. You can’t use more than 13 pending
(opened) parentheses at the same time.
For example, suppose you want to calculate:
)
1
5
(
8
−
Keying 8 ÷ 5 – 1 will calculate 8 ÷ 5 first and then the result (1.6) will have 1
subtracted from it (resulting in 0.6), which is not what is intended.
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If you want to calculate
)
1
5
(
8
−
, use the following keystrokes:
Keystrokes
(ALG mode)
Display
OO 0.00 Clears any pending operations.
8zgØ5- 5.00 No calculation is done.
1gÙ 4.00 Calculates 5 − 1.
³ 2.00
Calculates
)
1
5
(
8
−
.
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 RPN
mode. 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 R0
through R9
and R.0
through R.9
. Still
other storage registers — referred to as the “financial registers” — are reserved for
numbers used in financial calculations.
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 R0
through R9
, 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.
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Example: Before you leave to call on a customer interested in your personal
computer, you store the cost of the computer ($1,250) and also the cost of a
printer ($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.
Keystrokes Display
1250?0 1,250.00 Stores the cost of the computer in R0
.
500?2 500.00 Stores the cost of the printer in R2
.
; Turns the calculator off.
Later that same day …
Keystrokes
(RPN mode)
Display
; 500.00 Turns the calculator back on.
:0 1,250.00 Recalls the cost of the computer to
the display.
6§ 7,500.00 Multiplies the quantity ordered to get
the cost of the computers.
:2 500.00 Recalls the cost of the printer to the
display.
+ 8,000.00 Total invoice.
Keystrokes
(ALG mode)
Display
; 500.00 Turns the calculator back on.
:0 1,250.00 Recalls the cost of the computer to
the display.
§6 6. Multiplies by the quantity ordered to
get the cost of the computers.
+:2 500.00 Recalls the cost of the printer to the
display.
³ 8,000.00 Total invoice.
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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.* This also clears the
display.
All storage registers are also cleared when Continuous Memory is reset (as
described on page 86).
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 R0
through R4.
Example: In the example on page 23, we updated the balance in your
checkbook. Let’s suppose that because data is stored indefinitely in your
calculator’s 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.
Keystrokes Display
58.33?0 58.33 Stores the current balance in register
R0
.
* fCLEARH is not programmable.
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Keystrokes Display
22.95?-0 22.95 Subtracts the first check from the
balance in R0
. Note that the display
continues to show the amount
subtracted; the answer is placed only
in R0
.
13.7?-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 R0
to check the
new balance.
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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
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:
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.
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.
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Percentages in ALG Mode
In ALG 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.
5. Press }.
For example, to find 14% of $300:
Keystrokes
(ALG mode)
Display
OO 0.00 Clears any pending operations.
300 300. Keys in the base number.
§ 300.00 Tells the calculator to multiply the 300
by the percentage entered next.
14 14. Keys in the percentage.
b 0.14 Divides the percentage by 100.
} 42.00 Calculates the amount.
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.)
Note: This is the last time the initial OO will be shown in these
examples. Don’t forget to clear the calculator in ALG mode before beginning
a new calculation.
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Net Amount in RPN Mode
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 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 $23,250. 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.
Keystrokes
(RPN mode)
Display
23250\ 23,250.00 Keys in the base amount and
separates it from the percentage.
8b 1,860.00 Amount of discount.
- 21,390.00 Base amount less discount.
6b 1,283.40 Amount of tax (on $21,390).
= 22,673.40 Total cost: base amount less discount
plus tax.
Net Amount in ALG Mode
In ALG mode, you can calculate a net amount all in one calculation:
For example, to decrease 200 by 25%, just enter 200-25b}. (Result is 150.)
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
1250+7b 87.50 Interest on the loan is $87.50.
} 1,337.50 You owe this amount at the end of
one year.
Example: You’re buying a new car that lists for $23,250. 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.
Keystrokes
(ALG mode)
Display
23250- 23,250.00 Keys in the base amount and
prepares to subtract the discount
percentage.
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Keystrokes
(ALG mode)
Display
8b 1,860.00 Amount of discount.
= 21,390.00 Base amount less discount.
6b 1,283.40 Amount of tax (on $21,390).
} 22,673.40 Total cost: base amount less discount
plus tax.
Percent Difference
In RPN or ALG 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 $58.50 to $53.25 per share. What is
the percent change? (Note that the \ key is the same as the } key in ALG
mode.)
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.
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,
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.
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Percent of Total in RPN Mode
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?
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.
In RPN mode, 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
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.
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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:
Keystrokes
(RPN mode)
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 % it is of
the number in the display.
Z 29.69 Europe had nearly 30% of the total
sales.
Percent of Total in ALG Mode
In ALG 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?
Keystrokes
(ALG 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 % it is of
the number in the display.
Z 29.69 Europe had nearly 30% of the total
sales.
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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:
Keystrokes
(ALG mode)
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.
Calendar Functions
The calendar functions provided by the hp 12c platinum — gD and
gÒ — can handle dates from October 15, 1582 through November 25,
4046. These calendar functions work the same in both RPN and ALG modes.
Date Format
For each of the calendar functions — and also for bond calculations (fE and
fS) — 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 gÕ. 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.
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For example, to key in April 7, 2004:
Keystrokes Display
4.072004 4.072004
Day-Month-Year. To set the date format to day-month-year, press gÔ. 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, 2004:
Keystrokes Display
7.042004 7.042004
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 gD 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.*
* 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.
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Example: If you purchased a 120-day option on a piece of land on 14 May
2004, what would be the expiration date? Assume that you normally express
dates in the day-month-year format.
Keystrokes Display
gÔ 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.)
14.052004\ 14.05 Keys in the date and separates it
from the number of days to be
entered.
120gD 11,09,2004 6 The expiration date is 11
September 2004, a Saturday.
When gD is executed as an instruction in a running program, the calculator
pauses for about 1 second to display the result, then resumes program execution.
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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 gÒ.
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, 2004 to October 14, 2005? Assume that
you normally express dates in the month-day-year format.
Keystrokes Display
gÕ 11.09 Sets date format to month-day-year.
(Display shown assumes date
remains from preceding example.)
6.032004\ 6.03 Keys in the earlier date and
separates it from the later date.
10.142005gÒ 498.00 Keys in the later date. Display shows
actual number of days.
~ 491.00 Number of days counted on the
basis of a 30-day month.
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Section 3
Basic Financial Functions
The Financial Registers
In addition to the data storage registers discussed on page 27, 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.*
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.†
* 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, $, P, M, gA, or gC), pressing one of these five keys calculates the
corresponding value and stores it into the corresponding register; otherwise pressing one of
these five keys merely stores the number from the display into the corresponding register.
† It’s good practice to press the corresponding key twice after :, since often you may want
to calculate a financial value right after displaying another financial value. As indicated in
the preceding footnote, if you wanted to display FV and then calculate PV, for example, you
should press :MM$. 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.
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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.
The financial registers are also cleared when you press fCLEARH and when
Continuous Memory is reset (as described on page 86).
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 + in RPN mode or
+~} in ALG mode.
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$.*
4. Press fÏ 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. In RPN mode, press + or in ALG mode, press +~} to calculate the
total of the principal and the accrued interest shown in the display.
The quantities n, i, and PV can be entered in any order.
* 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 (see page 46), which is applicable primarily to compound
interest calculations.
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Example 1: Your good friend needs a loan to start his latest enterprise and has
requested that you lend him $450 for 60 days. You lend him the money at 7%
simple interest, to be calculated on a 360-day basis. What is the amount of
accrued interest he will owe you in 60 days, and what is the total amount owed?
Keystrokes
(RPN mode)
Display
60n 60.00 Stores the number of days.
7¼ 7.00 Stores the annual interest rate.
450Þ$ –450.00 Stores the principal.
fÏ 5.25 Accrued interest, 360-day basis.
+ 455.25 Total amount: principal plus accrued
interest.
In ALG mode, perform the steps in the RPN listing above, except replace the last
step with the step below.
Keystrokes
(ALG mode)
Display
+~} 455.25 Total amount: principal plus accrued
interest.
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
basis. What is the amount of accrued interest he will owe you in 60 days, and
what is the total amount owed?
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.
In ALG mode, perform the steps in the RPN listing above, except replace the last
step with the step below.
Keystrokes
(ALG mode)
Display
+~} 455.18 Total amount: principal plus accrued
interest.
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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 the time line when
the transaction occurs; money you pay out is represented by an arrow pointing
down.
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:
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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
63 through 67). 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.
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 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.)
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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
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 g× if payments are made at the beginning of the compounding
periods.
z Press g if payments are made at the end of the compounding periods.
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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.
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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 into n. The same
is true for i. Values of n and i are calculated and stored like this in Example 2 on
page 59.
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 gA and gC keys are used in Example 1
on page 59.
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 gC.
3. Enter at least two of the following values:
z Present value, using $.
z Payment amount, using P.
z Future value, using M.
Note: Remember to observe
the cash flow sign
convention.
4. If a PMT was entered, press g× or g to set the payment mode.
5. Press n to calculate the number of payments or periods.
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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.* 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.†
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 $325
payments at the end of each month, how many payments will be required to pay
off the loan, and how many years will this take?
Keystrokes
(RPN mode)
Display
fCLEARG
10.5gC 0.88 Calculates and stores i.
35000$ 35,000.00 Stores PV.
325ÞP –325.00 Stores PMT (with minus sign for cash
paid out).
g –325.00 Sets the payment mode to End.
* The calculator will round n down to the next lower integer if the fractional portion of n is less
than 0.005.
† After calculating n, pressing ¼,$,P, or M will recalculate the value in the
corresponding financial register.

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