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

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

File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 2 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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

3 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 3 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

4 Introduction File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 4 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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

5 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 5 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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

6 Contents File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 6 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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

Contents 7 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 7 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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

8 Contents File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 8 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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

Contents 9 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 9 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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

10 Contents File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 10 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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

Contents 11 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 11 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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

12 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 12 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

Making Financial Calculations Easy 13 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 13 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

14 Making Financial Calculations Easy File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 14 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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. gÂ 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.

File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 15 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm Part I Problem Solving

16 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 16 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

Section 1: Getting Started 17 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 17 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

18 Section 1: Getting Started File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 18 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

Section 1: Getting Started 19 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 19 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

20 Section 1: Getting Started File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 20 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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”.

Section 1: Getting Started 21 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 21 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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 (.)

22 Section 1: Getting Started File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 22 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

Section 1: Getting Started 23 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 23 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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).

24 Section 1: Getting Started File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 24 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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:

Section 1: Getting Started 25 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 25 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

26 Section 1: Getting Started File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 26 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

Section 1: Getting Started 27 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 27 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

28 Section 1: Getting Started File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 28 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

Section 1: Getting Started 29 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 29 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

30 Section 1: Getting Started File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 30 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

31 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 31 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

32 Section 2: Percentage and Calendar Functions File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 32 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

Section 2: Percentage and Calendar Functions 33 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 33 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

34 Section 2: Percentage and Calendar Functions File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 34 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

Section 2: Percentage and Calendar Functions 35 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 35 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

36 Section 2: Percentage and Calendar Functions File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 36 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

Section 2: Percentage and Calendar Functions 37 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 37 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

38 Section 2: Percentage and Calendar Functions File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 38 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

Section 2: Percentage and Calendar Functions 39 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 39 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

40 Section 2: Percentage and Calendar Functions File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 40 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

41 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 41 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

42 Section 3: Basic Financial Functions File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 42 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

Section 3: Basic Financial Functions 43 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 43 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

44 Section 3: Basic Financial Functions File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 44 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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:

Section 3: Basic Financial Functions 45 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 45 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.)

46 Section 3: Basic Financial Functions File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 46 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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 gÂ if payments are made at the end of the compounding periods.

Section 3: Basic Financial Functions 47 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 47 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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.

48 Section 3: Basic Financial Functions File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 48 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm

Section 3: Basic Financial Functions 49 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 49 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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 gÂ to set the payment mode. 5. Press n to calculate the number of payments or periods.

50 Section 3: Basic Financial Functions File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 50 of 275 Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm 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). gÂ –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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