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hp 12c financial calculator
user's guide
H
Edition 4
HP Part Number 0012C-90001
File name: hp 12c_user's guide_English_HDPMBF12E44
Printed Date: 2005/7/29
Page: 1 of 209
Dimension: 14.8 cm x 21 cm

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Table of Contents

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   Summary of Contents for HP 12c

  • Page 1 12c financial calculator user's guide Edition 4 HP Part Number 0012C-90001 File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 1 of 209 Printed Date: 2005/7/29 Dimension: 14.8 cm x 21 cm...
  • Page 2 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.
  • Page 3: Introduction

    Introduction About This Handbook This hp 12c user's guide is intended to help you get the most out of your investment in your hp 12c 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,”...
  • Page 4: Financial Calculations In The United Kingdom

    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 Solutions Handbook. Included are solutions to problems in lending, forecasting, pricing, statistics, savings, investment analysis, personal finance, securities, Canadian mortgages, learning curves in manufacturing, and queuing theory.
  • Page 5: Table Of Contents

    Contents Introduction..............3 About This Handbook ..............3 Financial Calculations in the United Kingdom........4 For More Solutions to Financial Problems...........4 Problem Solving ......... 15 Part I. Section 1: Getting Started..........16 Power On and Off................16 Low-Power Indication..............16 The Keyboard ................16 Keying in Numbers ..............17 Digit Separators ..............17 Negative Numbers ..............17 Keying in Large Numbers ............18...
  • Page 6 Contents Clearing the Financial Registers ..........33 Simple Interest Calculations............33 Financial Calculations and the Cash Flow Diagram......34 The Cash Flow Sign Convention..........36 The Payment Mode ............... 37 Generalized Cash Flow Diagrams ........... 37 Compound Interest Calculations............. 39 Specifying the Number of Compounding Periods and the Periodic Interest Rate .................
  • Page 7: Contents

    Contents Section 6: Statistics Functions ........76 Accumulating Statistics ..............76 Correcting Accumulated Statistics ...........77 Mean ..................77 Standard Deviation...............79 Linear Estimation ................80 Weighted Mean................81 Section 7: Mathematics and Number-Alteration Functions 83 One-Number Functions ..............83 The Power Function ...............85 Programming ..........87 Part II.
  • Page 8 Contents Section 11: Multiple Programs ........120 Storing Another Program ............120 Running Another Program............122 Solutions ..........123 Part III. Section 12: Real Estate and Lending ......124 Annual Percentage Rate Calculations With Fees......124 Price of a Mortgage Traded at a Discount or Premium....126 Yield of a Mortgage Traded at a Discount or Premium ....
  • Page 9: Contents

    Contents Appendixes ..............169 Appendix A: The Automatic Memory Stack ....170 Getting Numbers Into the Stack: The Key......171 Termination of Digit Entry .............172 Stack Lift................172 Rearranging Numbers in the Stack ..........172 key ..............172 Key ...............172 One-Number Functions and the Stack ...........173 Two-Number Functions and the Stack..........173 Mathematics Functions ............173 Percentage Functions ............
  • Page 10 Contents 30/360 Day Basis.............. 187 Bonds ..................188 Depreciation ................189 Straight-Line Depreciation............. 189 Sum-of-the-Years-Digits Depreciation ........189 Declining-Balance Depreciation ..........190 Modified Internal Rate of Return........... 190 Advance Payments..............190 Interest Rate Conversions ............191 Finite Compounding............191 Continuous Compounding............ 191 Statistics ...................
  • Page 11 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. While working through the examples below, don’t be concerned about learning how to use the calculator;...
  • Page 12 Making Financial Calculations Easy Note: A battery symbol ( ) shown in the lower-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 E. The calendar functions and nearly all of the financial functions take some time to produce an answer.
  • Page 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. To begin learning about this powerful financial tool, just turn the page. File name: hp 12c_user's guide_English_HDPMBF12E44...
  • Page 15: Part I. Problem Solving

    Part I Problem Solving File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 15 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm...
  • Page 16: Getting Started

    Appendix E. The Keyboard Many keys on the hp 12c 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.
  • Page 17: Keying In Numbers

    Section 1: Getting Started Throughout this handbook, references to the operation of an alternate function appear as only the function name in a box (for example, “The L function …”). References to the selection of an alternate function appear preceded by the appropriate prefix key (for example, “Pressing fL …”).
  • Page 18: Keying In Large Numbers

    The CLEAR Keys Clearing a register or the display replaces the number in it with zero. Clearing program memory replaces the instructions there with gi00. There are several clearing operations on the hp 12c, as shown in the table below: Key(s) Clears: Display and X-register.
  • Page 19: Simple Arithmetic Calculations

    Any simple arithmetic calculation involves two numbers and an operation — addition, subtraction, multiplication, or division. To do such a calculation on your hp 12c, 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.
  • Page 20: Chain Calculations

    The hp 12c 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.”...
  • Page 21 The preceding example demonstrates how the hp 12c 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.
  • Page 22 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 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.
  • Page 23: Storage Registers

    Section 1: Getting Started Storage Registers Numbers (data) in the hp 12c 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”...
  • Page 24: Clearing Storage Registers

    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 enables you to do all this in a single operation: 1.
  • Page 25 Section 1: Getting Started Storage register arithmetic is possible with only registers R through R Example: In the example on page 20, 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.
  • Page 26: Percentage And Calendar Functions

    Functions Percentage Functions The hp 12c 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;...
  • Page 27: Section 2: Percentage And Calendar Functions

    A net amount — that is, the base amount plus or minus the percentage amount — can be calculated easily with your hp 12c, 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 -.
  • Page 28: Percent Of Total

    Europe had nearly 30% of the total sales. The hp 12c 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.
  • Page 29: Calendar Functions

    Europe had nearly 30% of the total sales. Calendar Functions The calendar functions provided by the hp 12c — D and Ò — can handle dates from October 15, 1582 through November 25, 4046. Date Format For each of the calendar functions —...
  • Page 30: Future Or Past Dates

    Section 2: Percentage and Calendar Functions File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 30 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm...
  • Page 31: Number Of Days Between Dates

    (the extra days occurring in leap years), if any. In addition, the hp 12c 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 ~.
  • Page 32: Basic Financial Functions

    Basic Financial Functions The Financial Registers In addition to the data storage registers discussed on page 23, the hp 12c 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...
  • Page 33: Clearing The Financial Registers

    Continuous Memory is reset (as described on page 70). Simple Interest Calculations The hp 12c 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 +.
  • Page 34: Financial Calculations And The Cash Flow Diagram

    Section 3: Basic Financial Functions Keystrokes Display 7.00 7¼ Stores the annual interest rate. –450.00 450Þ$ Stores the principal. fÏ 5.25 Accrued interest, 360-day basis. 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.
  • Page 35 Section 3: Basic Financial Functions 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.
  • Page 36: The Cash Flow Sign Convention

    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 Solutions Handbook.) FV — the future value — is the final cash flow or the compounded value of a series of prior cash flows.
  • Page 37: The Payment Mode

    Section 3: Basic Financial Functions 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).
  • Page 38 Section 3: Basic Financial Functions File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 38 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm...
  • Page 39: Compound Interest Calculations

    Section 3: Basic Financial Functions 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.
  • Page 40 Section 3: Basic Financial Functions If the answer calculated is not an integer (that is, there would be nonzero digits to the right of the decimal point), the calculator rounds the answer up to the next higher integer before storing it in the n register and displaying it. For example, if n were calculated as 318.15, 319.00 would be the displayed answer.
  • Page 41 Section 3: Basic Financial Functions Keystrokes Display 27.33 Twenty-seven years and four months. Because the calculator rounds the calculated value of n up to the next higher integer, in the preceding example it is likely that — while 328 payments will be required to pay off the loan —...
  • Page 42 Section 3: Basic Financial Functions Example 2: You’re opening a savings account today (the middle of the month) with a $775 deposit. The account pays 6 % interest compounded semimonthly. If you make semimonthly deposits of $50 beginning next month, how long will it take for your account to reach $4000 ? Keystrokes Display...
  • Page 43: Calculating The Periodic And Annual Interest Rates

    Section 3: Basic Financial Functions Keystrokes Display 4,027.27 Calculates FV – which equals the balance in the account if 58 full deposits were made. –50.00 Recalls amount of deposits. 3,977.27 Calculates the balance in the account if 57 full deposits were made and interest accrued during the 58 month.
  • Page 44: Calculating The Present Value

    Section 3: Basic Financial Functions Example: What annual interest rate must be obtained to accumulate $10,000 in 8 years on an investment of $6,000 with quarterly compounding ? Keystrokes Display fCLEARG 32.00 8\4§w Calculates and stores n. –6,000.00 6000Þ$ Stores PV (with minus sign for cash paid out).
  • Page 45 Section 3: Basic Financial Functions Example 1: You’re financing a new car purchase with a loan from an institution that requires 15% interest compounded monthly over the 4-year term of the loan. If you can make payments of $150 at the end of each month and your down payment will be $1,500, what is the maximum price you can pay for the car ? (Assume the purchase date is one month prior to the date of the first payment.) Keystrokes...
  • Page 46: Calculating The Payment Amount

    Section 3: Basic Financial Functions Keystrokes Display fCLEARG 5.00 Stores n. 12.00 12¼ Stores i. 17,500.00 17500P Stores PMT. Unlike in the previous problem, here PMT is positive since it represents cash received. 540,000.00 540000M Stores FV. 540,000.00 g Sets payment mode to End. –369,494.09 The maximum purchase price to provide a 12% annual yield.
  • Page 47 Section 3: Basic Financial Functions Keystrokes Display fCLEARG 348.00 29gA Calculates and stores n. 1.19 14.25gC Calculates and stores i. 43,400.00 43400$ Stores PV. 43,400.00 g Sets payment mode to End. –523.99 Monthly payment (with minus sign for cash paid out). Example 2: Looking forward to retirement, you wish to accumulate $60,000 after 15 years by making deposits in an account that pays 9 % interest...
  • Page 48: Calculating The Future Value

    Section 3: Basic Financial Functions Calculating the Future Value 1. Press fCLEARG to clear the financial registers. 2. Enter the number of payments or periods, using n or A. 3. Enter the periodic interest rate, using ¼ or C. 4. Enter either or both of the following: Note: Remember to Present value, using $.
  • Page 49 Section 3: Basic Financial Functions Example 2: If you deposit $50 a month (at the beginning of each month) into a new account that pays 6 % annual interest compounded monthly, how much will you have in the account after 2 years ? Keystrokes Display fCLEARG...
  • Page 50: Odd-period Calculations

    Section 3: Basic Financial Functions File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 50 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm...
  • Page 51 Section 3: Basic Financial Functions You can calculate i, PV, PMT, and FV for transactions involving an odd period simply by entering a noninteger n. (A noninteger is a number with at least one nonzero digit to the right of the decimal point.) This places the calculator in Odd-Period mode.
  • Page 52 Section 3: Basic Financial Functions Example 1: A 36-month loan for $4,500 accrues interest at a 15% annual percentage rate (APR), with the payments made at the end of each month. If interest begins accruing on this loan on February 15, 2004 (so that the first period begins on March 1, 2004), calculate the monthly payment, with the odd days counted on the basis of a 30-day month and compound interest used for the odd period.
  • Page 53 Section 3: Basic Financial Functions Example 2: A 42-month car loan for $3,950 began accruing interest on July 19, 2004, so that the first period began on August 1, 2004. Payments of $120 are made at the end of each month. Calculate the annual percentage rate (APR), using the actual number of odd days and simple interest for the odd period.
  • Page 54: Amortization

    This rounding affects the number inside the calculator as well as how the number appears in the display. The amounts calculated on your hp 12c may differ from those on the statements of lending institutions by a few cents, since different rounding techniques are sometimes used.
  • Page 55 The number of payments keyed in just before f! is pressed is taken to be the payments following any that have already been amortized. Thus, if you now press 12f!, your hp 12c will calculate the amounts applied to interest and to the principal from the second year’s payments (that is, the second 12 months):...
  • Page 56 Section 3: Basic Financial Functions Keystrokes Display –552.08 Portion of first payment applied to interest. –21.27 Portion of first payment applied to principal. –551.85 Portion of second payment applied to interest. –21.50 Portion of second payment applied to principal. 2.00 Total number of payments amortized.
  • Page 57: Additional Financial Functions

    Functions Discounted Cash Flow Analysis: NPV and IRR The hp 12c provides functions for the two most widely-used methods of discounted cash flow analysis: l (net present value) and L (internal rate of return). These functions enable you to analyze financial problems involving cash flows (money paid out or received) occurring at regular intervals.
  • Page 58: Calculating Net Present Value (npv)

    Section 4: Additional Financial Functions If NPV is positive, the financial value of the investor’s assets would be increased: the investment is financially attractive. If NPV is zero, the financial value of the investor’s assets would not change: the investor is indifferent toward the investment. If NPV is negative, the financial value of the investor’s assets would be decreased: the investment is not financially attractive.
  • Page 59 Section 4: Additional Financial Functions The amounts of the subsequent cash flows are stored – in the order they occur – in the remaining storage registers: CF thru CF in R thru R , and CF thru CF in R thru R , respectively.
  • Page 60 Section 4: Additional Financial Functions Example: An investor has an opportunity to buy a duplex for $80,000 and would like a return of at least 13%. He expects to keep the duplex 5 years and then sell it for $130,000; and he anticipates the cash flows shown in the diagram below.
  • Page 61 Grouped Cash Flows. A maximum of 20 cash flow amounts (in addition to the initial investment CF ) can be stored in the hp 12c. However, problems involving more than 20 cash flows can be handled if among the cash flows there are equal consecutive cash flows. For such problems, you merely enter along with the amounts of the cash flows the number of times —...
  • Page 62 Section 4: Additional Financial Functions Example: An investor has an opportunity to purchase a piece of property for $79,000; and he would like a 13 % return. He expects to be able to sell it after 10 years for $100,000 and anticipates the yearly cash flows shown in the table below: Year Cash Flow...
  • Page 63: Calculating Internal Rate Of Return (irr)

    Section 4: Additional Financial Functions Calculating Internal Rate of Return (IRR) 1. Enter the cash flows using either of the methods described above under Calculating Net Present Value. 2. Press fL. The calculated value of IRR appears in the display and also is automatically stored in the i register.
  • Page 64: Reviewing Cash Flow Entries

    Section 4: Additional Financial Functions The complex mathematical characteristics of the IRR computation have an additional ramification: Depending on the magnitudes and signs of the cash flows, the computation of IRR may have a single answer, multiple answers, a negative answer or no answer.
  • Page 65: Changing Cash Flow Entries

    Section 4: Additional Financial Functions Keystrokes Display 2.00 7.00 Resets the number in the n register to its original value. To display all the cash flow amounts and the number of times they occur consecutively: Keystrokes Display 1.00 100,000.00 1.00 4,500.00 2.00 9,000.00...
  • Page 66: Bond Calculations

    –1,857.21 The new NPV. Bond Calculations The hp 12c enables you to solve for bond price (and the interest accrued since the The E and S calculations are last interest date) and the yield to maturity. †...
  • Page 67: Bond Price

    Section 4: Additional Financial Functions To calculate bond price and yield for a 30/360 bond (that is, using the basis of a 30day month and a 360-day year — such as for municipal bonds, corporate bonds, and state and local government bonds), and to calculate bond price for bonds with an annual coupon payment, refer to Section 16: Bonds.
  • Page 68: Depreciation Calculations

    4.28 4.282004\ Enters settlement (purchase) date. 6.042018 6.042018 Enters maturity (redemption) date. 8.15 Bond yield. Depreciation Calculations The hp 12c enables you to calculate depreciation and the remaining depreciable value (book value minus salvage value) using straight-line, sum-of-the-years-digits, and declining-balance methods. To do so with any of these methods: 1.
  • Page 69 Section 4: Additional Financial Functions Example: A metalworking machine, purchased for $10,000, is depreciated over 5 years. Its salvage value is estimated at $500. Find the depreciation and remaining depreciable value for the first 3 years of the machine’s life using the declining-balance method at double the straight-line rate (200 percent declining-balance).
  • Page 70: Additional Operating Features

    Section 5 Additional Operating Features Continuous Memory The calculator’s Continuous Memory contains the data storage registers, the financial registers, the stack and LAST X registers, program memory, and status information such as display format, date format, and payment mode. All information in Continuous Memory is preserved even while the calculator is turned off.
  • Page 71: Section 5: Additional Operating Features

    19.87 19.8745632\ 14.87 Although you see only two decimal places, all calculations in your hp 12c are performed with full 10-digit numbers. When only two decimal places are displayed, numbers are rounded to two decimal places: if the third digit is 5 through 9, the second digit is increased by one;...
  • Page 72: Scientific Notation Display Format

    Section 5: Additional Operating Features Keystrokes Display 14.8746 14.9 14.87456320 Although nine decimal places were specified after f, only eight are displayed since the display can show a total of only 10 digits. The standard display format, plus the specified number of decimal places, remain in effect until you change them;...
  • Page 73: Special Displays

    Section 5: Additional Operating Features Keystrokes Display 1.487456 01 The exponent in this example indicates that the decimal point should be moved one decimal place to the right, giving the number 14.87456, which is the first seven digits of the number previously in the display. To set the display back to standard display format, press f followed by the desired number of decimal places.
  • Page 74: The Key

    Section 5: Additional Operating Features Errors. If you attempt an improper operation — such as division by zero — the calculator will display the word Error followed by a digit (0 through 9). To clear the Error File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 74 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm...
  • Page 75: Arithmetic Calculations With Constants

    Section 5: Additional Operating Features Arithmetic Calculations With Constants Example: At Permex Pipes a certain pipe fitting is packaged in quantities of 15, 75, and 250. If the cost per fitting is $4.38, calculate the cost of each package. Keystrokes Display 15.00 Keys first quantity into calculator.
  • Page 76: Statistics Functions

    Section 6 Statistics Functions Accumulating Statistics The hp 12c can perform one- or two-variable statistical calculations. The data is entered into the calculator using the _ key, which automatically calculates and stores statistics of the data into storage registers R , through R .
  • Page 77: Correcting Accumulated Statistics

    Section 6: Statistics Functions The table below shows where the accumulated statistics are stored. Register Statistic (and display) n: number of data pairs accumulated. Σx: summation of x-values. Σx : summation of squares of x-values. Σy: summation of y-values. Σy summation of squares of y-values.
  • Page 78 Section 6: Statistics Functions Salesperson Hours/Week Hours/Week $17,000 $25,000 $26,000 $20,000 $21,000 $28,000 $15,000 To find the average workweek and sales of this sample: Keystrokes Display 0.00 fCLEAR² Clears statistics registers. 32.00 1.00 17000_ First entry. 40.00 2.00 25000_ Second entry. 45.00 3.00 26000_...
  • Page 79: Standard Deviation

    Standard deviation of sales. 6.03 Standard deviation of hours worked. The formulas used in the hp 12c for calculating s , and s give best estimates of the population standard deviation based on a sample of the population. Thus, current statistical convention calls them sample standard deviations.
  • Page 80: Linear Estimation

    Section 6: Statistics Functions Linear Estimation With two-variable statistical data accumulated in the statistics registers, you can y ˆ x ˆ estimate a new y-value ( ) given a new x-value, and estimate a new x-value ( given a new y-value. y ˆ...
  • Page 81: Weighted Mean

    Section 6: Statistics Functions Example: Compute the slope and intercept of the regression line in the preceding example. Keystrokes Display 15.55 y-intercept (A); projected value for x = 0. 0.001 1 gR~d~- Slope of the line (B); indicates the change in the projected values caused by an incremental change in the x value.
  • Page 82 1.19 Weighted mean cost per gallon. A procedure for calculating the standard deviation and standard error (as well as the mean) of weighted or grouped data is included in the hp 12c Solutions Handbook. File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 82 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm...
  • Page 83: Mathematics And Number-alteration Functions

    Section 7 Mathematics and Number-Alteration Functions The hp 12c provides several keys for mathematical functions and for altering, numbers. These functions are useful for specialized financial calculations as well as for general mathematics calculations. One-Number Functions Most of the mathematics functions require that only one number be in the calculator (that is, the number in the display) before the function key is pressed.
  • Page 84: Section 7: Mathematics And Number-alteration Functions

    Section 7: Mathematics and Number-Alteration Functions Fractional. Pressing gT replaces the number in the display by its fractional portion — that is, it replaces all digits to the left of the decimal point by 0. Like Ñ, T changes the number inside the calculator as well as its displayed version.
  • Page 85: The Power Function

    Section 7: Mathematics and Number-Alteration Functions The Power Function Pressing q calculates a power of a number — that is, y . Like the arithmetic function +, q requires two numbers: 1. Key in the base number (which is designated by the y on the key). 2.
  • Page 87: Programming

    Part II Programming File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 87 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm...
  • Page 88: Programming Basics

    Section 8 Programming Basics Why Use Programs? A program is simply a sequence of keystrokes that is stored in the calculator. Whenever you have to calculate with the same sequence of keystrokes several times, you can save a great deal of time by incorporating these keystrokes in a program.
  • Page 89: Running A Program

    Section 8: Programming Basics Keystrokes Display 150.00 Price less discount. Handling charge. 155.00 Net cost (price less discount plus handling charge). Next, set the calculator to Program mode and erase any program(s) already stored: Keystrokes Display Sets calculator to Program mode. fCLEARÎ...
  • Page 90: Program Memory

    Section 8: Programming Basics Example: Run the program created above to calculate the net cost of a typewriter listing for $625 and an executive chair listing for $159. Keystrokes Display 155.00 Sets calculator to Run mode. Display shows number previously calculated. 625.
  • Page 91: Identifying Instructions In Program Lines

    Section 8: Programming Basics Identifying Instructions in Program Lines Each key on the hp 12c keyboard — except for the digit keys 0 through 9 — is identified by a two-digit “keycode” that corresponds to the key’s position on the keyboard.
  • Page 92: Displaying Program Lines

    Occasionally you’ll want to check several or all of the instructions stored in program memory. The hp 12c enables you to review program instructions either forward or backward through program memory: Pressing Ê (single step) while the calculator is in Program mode advances the calculator to the next line in program memory, then displays that line number and the keycode of the instruction stored there.
  • Page 93: The 00 Instruction And Program Line 00

    Section 8: Programming Basics Program line 07 contains the last instruction you keyed into program memory. However, if you press Ê again, you’ll see that this is not the last line stored in program memory: Keystrokes Display 08- 43, 33 Ê...
  • Page 94: Expanding Program Memory

    Section 8: Programming Basics Expanding Program M emory If no instructions have been keyed into program memory, if Continuous Memory has been reset, or if fCLEARÎ has been pressed (in Program mode), program memory consists of 8 program lines, and there are 20 storage registers available for storage of data.
  • Page 95: Setting The Calculator To A Particular Program Line

    Section 8: Programming Basics Program memory is automatically expanded like this whenever another seven instructions have been keyed into program memory — that is, when you key an instruction into program line 16, 23, 30 etc. In each case, the additional program lines made available are converted, seven lines at a time, from the last available data storage register (whether or not data has been stored in that register;...
  • Page 96: Executing A Program One Line At A Time

    Section 8: Programming Basics With the calculator in Run mode, pressing gi followed by two digit keys sets the calculator to the program line specified by the digit keys. Since the calculator is not in Program mode, the line number and keycode are not displayed.
  • Page 97: Interrupting Program Execution

    Interrupting Program Execution Occasionally you’ll want a program to stop executing so that you can see an intermediate result or enter new data. The hp 12c provides two functions for doing so: u (pause) and t (run/stop). Pausing During Program Execution When a running program executes a u instruction, program execution halts for about 1 second, then resumes.
  • Page 98 Section 8: Programming Basics Example: Create a program that calculates the entries in the AMOUNT, TAX, and TOTAL columns for each item on the jewelry distributor’s invoice shown on the next page, and also calculates the total in each of these columns for all items on the invoice.
  • Page 99 Section 8: Programming Basics Pressing the gu keys is not necessary when we do the calculations manually, since in Run mode the result of every intermediate calculation is displayed automatically; but we’ll include u instructions in the program so that the intermediate results AMOUNT and TAX are automatically displayed when the program is executed.
  • Page 100 100 Section 8: Programming Basics Keystrokes Display Pauses to display TAX. 07- 44 40 09- 44 40 Now, to run the program: Keystrokes Display 950.61 Sets calculator to Run mode. 0.00 fCLEAR² Clears registers R – R 6.75?0 Stores tax rate. 68.5 13\68.5 Enters quantity and price of first...
  • Page 101: Stopping Program Execution

    Section 8: Programming Basics If the duration of the pause is not long enough to write down the number displayed, you can prolong it by using more than one u instruction. Alternatively, you can have the program automatically stop as described next. Stopping Program Execution Stopping Program Execution Automatically.
  • Page 102 102 Section 8: Programming Basics Keystrokes Display 24\85 Third item. 2,040.00 AMOUNT for third item. 137.70 TAX for third item. 2,177.70 TOTAL for third item. 345. 5\345 Fourth item. 1,725.00 AMOUNT for fourth item. 116.44 TAX for fourth item. 1,841.44 TOTAL for fourth item.
  • Page 103: Branching And Looping

    Section 9 Branching and Looping Although the instructions in a program normally are executed in order of their program line numbers, in some situations it is desirable to have program execution transfer or “branch” to a program line that is not the next line in program memory. Branching also makes it possible to automatically execute portions of a program more than once —...
  • Page 104: Looping

    104 Section 9: Branching and Looping Looping If a i instruction specifies a lower-numbered line in program memory, the instructions in the program lines between the specified line and the i instruction will be executed repeatedly. As can be seen in the illustration above under Simple Branching, once the program begins executing the “loop”...
  • Page 105 Section 9: Branching and Looping Keystrokes Display Recalls the number of payments to be amortized. This program line is the one to which program execution will later branch. It is included because after the first time the loop is executed, the number in the “display”...
  • Page 106 106 Section 9: Branching and Looping Keystrokes Display Ê Line 02: :0. This is the beginning of the first pass through the loop. 1.00 Ê Line 03: f!. –531.25 Portion of first month’s payment applied to interest. Ê Line 04: gu. –531.25 Ê...
  • Page 107: Conditional Branching

    The hp 12c provides two conditional test instructions that are used in programs for conditional branching: o tests whether the number in the X-register (represented by the x in the key symbol) is less than or equal to the number in the Y-register (represented by the y in the key symbol).
  • Page 108 108 Section 9: Branching and Looping The program line immediately following that containing the conditional test instruction can contain any instruction; however, the most commonly used instruction there is i. If a i instruction follows a conditional test instruction, program execution branches elsewhere in program memory if the condition is true and continues with the next line in program memory if the condition is false.
  • Page 109 Section 9: Branching and Looping We’ll key the income into the display before running the program so that it will be in the X-register when the :0 instruction in program line 01 is executed. This instruction will place the test value 20,000 in the X-register and (as explained in Appendix A) move the income into the Y-register.
  • Page 110 110 Section 9: Branching and Looping Keystrokes Display 04- 43, 33 gi07 If condition is true, branches to program line 07. If condition is false, recalls 25% tax rate to X-register. 06- 43, 33 gi08 Branches to program line 08. Recalls 20% tax rate to X-register.
  • Page 111 Section 9: Branching and Looping Keystrokes Display 15,000.00 Ê Line 07: :1. 20.00 20% tax rate has been recalled to X-register, moving income to Y-register. Ê Line 08: b. 3,000.00 20% of 15,000 = 3,000. 20,000. 20000 Keys income equal to test value into display and X-register.
  • Page 112 112 Section 9: Branching and Looping Keystrokes Display Ê Line 02: ~. 25,000.00 Income has been placed in X-register and test value has been placed in Y-register. Ê Line 03: go. 25,000.00 Ê Condition tested by o was false, so program execution skipped the next line and continued at line 05: 25.00 25% tax rate has been recalled to...
  • Page 113: Program Editing

    Section 10 Program Editing There are various reasons why you might want to modify a program you have stored in Program memory: to correct a program that turns out to have errors; to insert new instructions such as ? to store intermediate results or u to display intermediate results;...
  • Page 115: Adding Instructions Within A Program

    Section 10: Program Editing Adding Instructions Within a Program If an instruction is to be added within a program, simply keying it in will replace the instruction previously stored in that program line, as described above; the contents of all higher-numbered program lines remain unchanged. To add instructions within a program, you could simply key in the new instructions, beginning at the proper program line, followed by the original instructions from that program line through the end of the program.
  • Page 116: Adding Instructions By Branching

    116 Section 10: Program Editing Example: Assuming you have added a - instruction at the end of program memory as in the preceding example, suppose you now wanted to insert an t instruction before the - instruction so that the program will display the amount of the tax before displaying the net income after tax.
  • Page 117 Section 10: Program Editing 5. Press gi00. This automatically converts a data storage register into seven additional lines of program memory (if there was not already a i00 instruction remaining at the end of program memory), and it ensures that program execution will branch to line 00 after the program is run. 6.
  • Page 118 118 Section 10: Program Editing Keystrokes Display Added instructions. 15- 43, 33 gi00 Keys in instruction immediately following point at which new instructions are being added. (This instruction was replaced in line 01 by i12 instruction.) 17- 43, 33 gi02 Branches back to second line (line 02) following point at which new instructions are being added.
  • Page 119 Section 10: Program Editing File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 119 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm...
  • Page 120: Multiple Programs

    Section 11 Multiple Programs You can store multiple programs in program memory, provided that you separate them by instructions that will halt program execution after each program is run and return to the beginning of the program if it is run again. You can run programs after the first one stored in program memory by setting the calculator to the first line of the program using i before pressing t.
  • Page 121 Section 11: Multiple Programs Example 1: Assuming that program memory still contains the last program from the preceding section (which consisted of 17 program lines), store after that program the office-supplies program from Section 8 (page 88). Since this is the second program to be stored in program memory, we’ll ensure that a i00 instruction separates it from the first program by doing step 3 in the procedure above.
  • Page 122: Running Another Program

    122 Section 11: Multiple Programs Example 2: With the two programs now stored in program memory from the preceding examples (occupying 27 program lines), store the amortization program from Section 9(page 103). Since there are already two programs stored in program memory, we’ll skip step 3 in the procedure above.
  • Page 123: Solutions

    Part III Solutions File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 123 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm...
  • Page 124: Real Estate And Lending

    Section 12 Real Estate and Lending Annual Percentage Rate Calculations With Fees Borrowers are usually charged fees in connection with the issuance of a mortgage, which effectively raises the interest rate. The actual amount received by the borrower (PV) is reduced, while the periodic payments remain the same. Given the life or term of the mortgage, the interest rate, the mortgage amount, and the basis of the fee charge (how the fee is calculated), the true Annual Percentage Rate (APR) may be calculated.
  • Page 125 Section 12: Real Estate and Lending Example 1: A borrower is charged 2 points for the issuance of his mortgage. If the mortgage amount is $60,000 for 30 years and the interest rate is 11 % per year, with monthly payments, what true annual percentage rate is the borrower paying ? (One point is equal to 1% of the mortgage amount.) Keystrokes Display...
  • Page 126: Price Of A Mortgage Traded At A Discount Or Premium

    126 Section 12: Real Estate and Lending Example 3: Again using the information given in example 1, what is the APR if the mortgage fee is stated as 2 points plus $150 ? Keystrokes Display g fCLEARG 360.00 30gA Months (into n) 0.96 11.5gC Percent monthly interest rate (into i).
  • Page 127 Section 12: Real Estate and Lending Example 1: A lender wishes to induce the borrower to prepay a low interest rate loan. The interest rate is 5% with 72 payments remaining of $137.17 and a balloon payment at the end of the sixth year of $2000. If the lender is willing to discount the future payments at 9%, how much would the borrower need to prepay the note ? Keystrokes...
  • Page 128: Yield Of A Mortgage Traded At A Discount Or Premium

    128 Section 12: Real Estate and Lending Yield of a Mortgage Traded at a Discount or Premium The annual yield of a mortgage bought at a discount or premium can be calculated given the original mortgage amount, interest rate, and periodic payment, as well as the number of payment periods per year, the price paid for the mortgage, and the balloon payment amount (if it exists).
  • Page 129 Section 12: Real Estate and Lending Keystrokes Display –79,000.00 79000Þ$ Input price of mortgage (into PV; negative to indicate money paid out). 0.97 ¼ Yield per month (calculated). 11.68 12§ Percent annual yield. Example 2: Using the same information given in example 1, calculate the annual yield if the loan is to be paid in full at the end of the fifth year (from original issuance).
  • Page 130: The Rent Or Buy Decision

    130 Section 12: Real Estate and Lending The Rent or Buy Decision The question of whether to rent or purchase a residence is not always easy to answer, especially when the time period over which you would own or rent a house is short.
  • Page 131 Section 12: Real Estate and Lending KEYSTROKES DISPLAY KEYSTROKES DISPLAY 144- File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 131 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm 1 44- 11527.612 81.66 0.437[(/F2 ]TJ1527.612 66.24 37[(/F2 ]TJ1527.612 85.74 37[(/F2 ]TJ1527.612 81.480...
  • Page 132 132 Section 12: Real Estate and Lending REGISTERS n: Period i: Apprec. PV: Price PMT: Used FV: Used : Period : Dwn Pmt : Life : i(Mtg) : Taxes/Mo : Improve. : Closing C. : % Comm. : Rent : Savings i : Bracket : Unused.
  • Page 133 Section 12: Real Estate and Lending 16. Press t to compute the yield on your investment in the house. 17. Press t to compute the value of a savings account or other investment. 18. Compare the value of the hypothetical savings account to the net proceeds of the sale of the house.
  • Page 134: Deferred Annuities

    134 Section 12: Real Estate and Lending Keystrokes Display 4.00 Years in investment. 10.00 10¼ Yearly appreciation rate. 70,000.00 70000$ House price. 32,391.87 NCPR (calculated). 19.56 Yield. 21,533.79 Balance in savings. By purchasing a house, you would gain $10,858.08 (32,391.87 – 21,533.79) over an alternate investment at 6.25% interest.
  • Page 135 Section 12: Real Estate and Lending Leases often call for periodic contractual adjustments of rental payments. For example, a 2-year lease calls for monthly payments (at the beginning of the month) of $500 per month for the first 6 months, $600 per month for the next 12 months, and $750 per month for the last 6 months.
  • Page 136: Investment Analysis

    — the amounts of depreciation in the first and last years are computed as fractions of a full year’s depreciation. Straight-Line Depreciation The following hp 12c program calculates the straight-line depreciation for the year desired with the acquisition date occurring at any time during the year. KEYSTROKES...
  • Page 137 Section 13: Investment Analysis KEYSTROKES DISPLAY KEYSTROKES DISPLAY 41-43, 33 gi30 REGISTERS n: Life i: Unused PV: Dep. Value PMT: Unused FV: Salvage : Used : #Mos./12 : Counter Yr. Dep. –R : Unused 1. Key in the program. 2. Press fCLEARG. 3.
  • Page 138 138 Section 13: Investment Analysis Note: If the number of months in the first calendar year is less than 12, the amount of depreciation in the 1st year will be less than a full year’s depreciation. The actual number of years that depreciation will occur is equal to the life +1.
  • Page 139: Declining-balance Depreciation

    Life. 1.00 1.00 4.5t First year: 504.75 depreciation. Declining-Balance Depreciation The following hp 12c program calculates the declining-balance depreciation for the year desired with the acquisition date occurring at any time during the year. KEYSTROKES DISPLAY KEYSTROKES DISPLAY fCLEARÎ gi31...
  • Page 140 140 Section 13: Investment Analysis KEYSTROKES DISPLAY KEYSTROKES DISPLAY 28-44 29-44 gi22 30-43, 33 § gi26 37-43, 33 REGISTERS n: Life i: Factor PV: Dep. Value PMT: Unused FV: Salvage : Used : #Mos./12 : Counter Yr. Dep. –R : Unused 1.
  • Page 141: Sum-of-the-years-digits Depreciation

    Life. 2.00 Year desired. 2.00 Second year: 11,458.33 depreciation. Sum-of-the-Years-Digits Depreciation The following hp 12c program calculates the sum-of-the-years-digits depreciation for the year desired with the acquisition date occurring at any time during the year. KEYSTROKES DISPLAY KEYSTROKES DISPLAY fCLEARÎ...
  • Page 142 142 Section 13: Investment Analysis KEYSTROKES DISPLAY KEYSTROKES DISPLAY fÝ 32-44 fÝ 33-44 34-43, 33 gi26 § gi30 41-43, 33 REGISTERS n: Life i: Unused PV: Dep. Value PMT: Unused FV: Salvage : Used : #Mos./12 : Counter Yr. Dep. –R : Unused 1.
  • Page 143 Section 13: Investment Analysis then press t. 7. Key in the number of months in first year The display will † show the amount of depreciation for the desired year. If desired, press ~ to see the remaining depreciable value, then press :$:3= ~-:M- to find the total depreciation through the current year.
  • Page 144: Full- And Partial-year Depreciation With Crossover

    When calculating declining-balance depreciation it is often advantageous for tax purposes to switch from declining balance to straight-line depreciation at some point. This hp 12c program calculates the optimum crossover point and automatically switches to straight-line depreciation at the appropriate time. The crossover point is the end of the year in which the declining-balance depreciation last exceeds or equals the amount of straight-line depreciation.
  • Page 145 Section 13: Investment Analysis KEYSTROKES DISPLAY KEYSTROKES DISPLAY § 70-44 71-44 73-44 76-44 78-44 79-44 80-44 gi39 32-43, 33 gi74 85-43, 33 40-44 41-44 File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 145 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm...
  • Page 146 146 Section 13: Investment Analysis KEYSTROKES DISPLAY KEYSTROKES DISPLAY 43-44 gi74 94-43, 33 gi58 95-43, 33 REGISTERS n: Life i: Factor PV: Dep. Value PMT: Unused FV: Salvage : Used : Dep. : Counter : Used Used Used Used 1. Key in the program. 2.
  • Page 147 Section 13: Investment Analysis Example: An electronic instrument is purchased for $11,000, with 6 months remaining in the current fiscal year. The instrument’s useful life is 8 years and the salvage value is expected to be $500. Using a 200% declining-balance factor, generate a depreciation schedule for the instrument’s complete life.
  • Page 148: Excess Depreciation

    148 Section 13: Investment Analysis Excess Depreciation When accelerated depreciation is used, the difference between total depreciation charged over a given period of time and the total amount that would have been charged under straight-line depreciation is called excess depreciation. To obtain excess depreciation: 1.
  • Page 149 Section 13: Investment Analysis This Modified Internal Rate of Return procedure (MIRR) is one of several IRR alternatives which avoids the drawbacks of the traditional IRR technique. The procedure eliminates the sign change problem and the reinvestment (or discounting) assumption by utilizing user stipulated reinvestment and borrowing rates.
  • Page 150 150 Section 13: Investment Analysis Keystrokes Display 657,152.37 10gCfl NPV of positive cash flows. Þ$ 775,797.83 20nM NFV of positive cash flows. 180000ÞgJ 0gK5ga 100000ÞK -660,454.55 6gCfl NPV of negative cash flows. 0.81 20n¼ Monthly MIRR 9.70 12§ Annual MIRR. File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 150 of 209 Printered Date: 2005/7/29...
  • Page 151: Leasing

    Section 14 Leasing Advance Payments Situations may exist where payments are made in advance (leasing is a good example). These agreements call for extra payments to be made when the transaction is closed. This first procedure finds the periodic payment amount necessary to achieve a desired yield when a number of payments are made in advance.
  • Page 152 152 Section 14: Leasing If solving for the payment amount will be done repetitively, key in the following hp 12c program. KEYSTROKES DISPLAY KEYSTROKES DISPLAY Þ fCLEARÎ g fCLEARG ¼ REGISTERS n: n–#Adv. Pmt. i: i PV: Used PMT: –1 FV: 0 : #Adv.
  • Page 153 Section 14: Leasing Example 2: Using the preceding program, solve for the monthly payment using the information given in example 1. Then change the yearly interest to 15% and solve for the new payment amount. Keystrokes Display 12.00 12?0 Duration of lease. 3.00 Number of advance payments.
  • Page 154: Solving For Yield

    154 Section 14: Leasing Solving for Yield To calculate the periodic yield, information is entered as follows: 1. Press g and fCLEARG. 2. Key in the total number of payments in the lease then press \. 3. Key in the total number of payments made in advance then press ?0-n.
  • Page 155 Section 14: Leasing If solving for yield will be done repetitively, key in the following hp 12c program: KEYSTROKES DISPLAY KEYSTROKES DISPLAY Þ fCLEARÎ g fCLEARG § ¼ 17-45, 43 REGISTERS n: n–#Adv. Pmts. i: i PV: Used PMT: Pmt.
  • Page 156: Advance Payments With Residual

    156 Section 14: Leasing Keystrokes Display 17.33 25000?3t Annual yield (as a percentage). 19.48 625?2t Annual yield (as a percentage) when PMT is increased $25. Advance Payments With Residual Situations may arise where a transaction has advance payments and a residual value (salvage value) at the end of the normal term.
  • Page 157 Section 14: Leasing REGISTERS n: Used. i: Interest PV: Used PMT: –1. FV: Residual : # Pmts (n) : Interest. : Loan. : Residual : # Adv. Pmt. : Used –R : Unused 1. Key in the program. 2. Key in the total number of payments then press ?0. 3.
  • Page 158: Solving For Yield

    158 Section 14: Leasing Example 2: Using the information from example 1, what would the monthly payments be if the lessor desired a yield of 18% annually ? Keystrokes Display 487.29 From previous example. 1.50 18\12z Monthly interest rate. 520.81 Monthly payment received by lessor.
  • Page 159 Section 14: Leasing Keystrokes Display –4,710.00 §=gJ Net amount of cash advanced. 34.00 145gK34ga Thirty-four cash flows of $145.00. 0.00 Thirty-fifth cash flow. 1,500.00 1500gK Thirty-sixth cash flow. 18.10 fL12§ Annual yield to lessor. File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 159 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm...
  • Page 160: Savings

    5.25 5.25\ Nominal rate. 1.31 4nz¼ Percent quarterly interest rate. 100Þ\ 5.35 Percent effective interest rate. For repeated calculations, the following hp 12c program can be used: KEYSTROKES DISPLAY KEYSTROKES DISPLAY fCLEARÎ gÂ Þ fCLEARG ¼ File name: hp 12c_user's guide_English_HDPMBF12E44...
  • Page 161: Effective Rate Converted To Nominal Rate

    Section 15: Savings REGISTERS n: # Periods. i: Nom. Rate/n PV: 0 PMT: Used. FV: Eff. Rate –R : Unused 1. Key in the program. 2. Key in the annual nominal rate as a percentage then press \. 3. Key in the number of compounding periods per year then press t to obtain the effective annual interest rate.
  • Page 162: Nominal Rate Converted To Continuous Effective Rate

    162 Section 15: Savings Nominal Rate Converted to Continuous Effective Rate This procedure converts a nominal annual interest rate to the continuous effective rate. 1. Press 1\. 2. Key in the nominal rate as a percentage then press b. 3. Press g>à. Example: What is the effective rate resulting from a 5 % passbook rate with continuous compounding ?
  • Page 163: Bonds

    Section 16 Bonds 30/360 Day Basis Bonds A bond is a contract to pay interest, usually semiannually, at a given rate (coupon) and to pay the principal of the bond at some specified future date. A bond which is calculated on a 30/360 day basis is one in which the day count basis is computed using 30 days in a month and 360 days in a year.
  • Page 164 164 Section 16: Bonds KEYSTROKES DISPLAY KEYSTROKES DISPLAY Þ ¼ § REGISTERS n: ∆ days/180 i: Yield/2 PV: Price PMT: Coupon/2. FV: Red+Cpn./2 : Yield : Price. : Coupon : Redemption : Coupon/2. –R : Unused 1. Key in the program. 2.
  • Page 165 Section 16: Bonds For a new case return to step 3. Note that only those values which have been changed need to be reentered and stored. 8. If yield is desired: a. Press 0?0. b. Key in the price as a percentage of par value and press ?1. c.
  • Page 166: Annual Coupon Bonds

    166 Section 16: Bonds Annual Coupon Bonds For bonds which have annual coupons, use the following hp 12c program to evaluate price and accrued interest on an Actual/Actual day basis. This program may be modified for annual coupon bonds to be calculated on a 30/360 day basis.
  • Page 167 Section 16: Bonds REGISTERS n: Used i: Yield PV: Used PMT: Cpn. or 0 FV: Used : # Periods (n) : Yield : Coupon : Redemption : Settlement : Next Cpn. : Last Coupon : Used –R : Unused For annual coupon bonds calculated on a 30/360 day basis, insert d after gÒ...
  • Page 169: Appendixes

    Appendixes File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 169 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm...
  • Page 170: Appendix A: The Automatic Memory Stack

    Appendix A The Automatic Memory Stack Four special registers in the hp 12c are used for storing numbers during calculations. To understand how these registers are used, they should be visualized as stacked on top of each other. (For this reason, they are generally referred to as the “stack registers” or collectively as “the stack.”) The stack registers are designated X, Y, Z, and T.
  • Page 171: Getting Numbers Into The Stack: The Key

    Appendix A: The Automatic Memory Stack Now let’s see what happens in the stack during a chain calculation: × × File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 171 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm...
  • Page 172: Termination Of Digit Entry

    172 Appendix A: The Automatic Memory Stack Termination of Digit Entry The first digit keyed in after digit entry has been terminated replaces the number already in the displayed X-register. Digit entry is automatically terminated when any key is pressed (except for digit entry keys — digit keys,., Þ, and É — and prefix keys —...
  • Page 173: One-number Functions And The Stack

    Appendix A: The Automatic Memory Stack Pressing d four times successively displays the numbers in the Y-, Z-, and T-registers and returns the numbers to their original registers. One-Number Functions and the Stack One-number mathematics and number-alteration functions — y, r, °, >, e, B, Ñ, and T —...
  • Page 174: Percentage Functions

    174 Appendix A: The Automatic Memory Stack When an arithmetic operation or q is performed, the answer is placed in the X-register, the number formerly in the X-register is copied into the LAST X register, and the stack drops. When the stack drops, the number in the Z-register is copied into the Y-register, and the number in the T-register is copied into the Z-register but also remains in the T-register.
  • Page 175: Calendar And Financial Functions

    Appendix A: The Automatic Memory Stack Calendar and Financial Functions The following table shows what quantity is in each stack register after the indicated calendar or financial function key is pressed. The symbols x, y, z, and t represent the number that was in the corresponding register (X, Y, Z, or T, respectively) at the time the function key was pressed.
  • Page 176: The Last X Register And The Key

    176 Appendix A: The Automatic Memory Stack The LAST X Register and the The number in the displayed X-register is copied into the LAST X register whenever any of the following function keys is pressed: § > ¿ Ñ à Ò...
  • Page 177: Arithmetic Calculations With Constants

    Appendix A: The Automatic Memory Stack The diagram on page 171 illustrates how the automatic stack lift and stack drop make chain calculations quick and error-free. Virtually every chain calculation you are likely to encounter can be done using only the four stack registers. However, to avoid having to store an intermediate result in a storage register, you should begin every chain calculation at the innermost number or pair of parentheses and then work outward —...
  • Page 178 178 Appendix A: The Automatic Memory Stack Keystrokes Display 84,000. 84000 Enters base amount into displayed X-register. 168,000.00 § Annual sales after first year. 336,000.00 § Annual sales after second year. 672,000.00 § Annual sales after third year. In the example above, the constant was repeatedly multiplied by the result of the previous operation, which was already in the displayed X-register.
  • Page 179: Appendix B: More About L

    IRR answer exists, and what that answer is. For the vast majority of cases, your hp 12c will find the unique IRR answer if it exists. But the IRR computation is so complex that if the cash flow sequence does not meet certain criteria, then sometimes the calculator is unable to determine whether or not an answer or answers exist.
  • Page 180 180 Appendix B: More About L Your guess will aid the calculator in its search, and if it finds an IRR answer near your guess, that answer will be displayed. Since the calculator cannot tell you the number of solutions that exist when there is more than one mathematically correct answer, you can continue to make guesses, pressing :gt after each one, to search for IRR solutions.
  • Page 181: Appendix C: Error Conditions

    Appendix C Error Conditions Some calculator operations cannot be performed under certain conditions (for example, z when x = 0). If you attempt such an operation under these conditions, the calculator will display the word Error followed by a digit, 0 through 9. Listed below are operations that cannot be performed under the conditions specified.
  • Page 182: Error 1: Storage Register Overflow

    182 Appendix C: Error Conditions Error 1: Storage Register Overflow Operation Condition ?+(0 through 4) ?-(0 through 4) Magnitude of result is greater than ?§(0 through 4) 9.999999999×10 ?z(0 through 4) Error 2: Statistics Operation Condition Ö n (number in R ) = 0 ...
  • Page 183: Error 5: Compound Interest

    Appendix C: Error Conditions Error 5: Compound Interest Operation Condition PMT ≤ –PV × i PMT = FV × i i ≤ –100 The values in i, PV, and FV are such that no solution exists for n. ¼ PMT = 0 and n < 0 Cash flows all have same sign.
  • Page 184: Error 7: Irr

    184 Appendix C: Error Conditions Error 7: IRR Refer to Appendix B. Error 8: Calendar Operation Condition Ò Improper date format or illegal date. Attempting to add days beyond calculator’s date capacity. Improper date format or illegal date. More than 500 years between settlement (purchase) date and maturity (redemption) date.
  • Page 185: Appendix D: Formulas Used

    Appendix D Formulas Used Percentage y × Base( Rate( ⎛ ⎞ − NewAmount( Base( ⎜ ⎟ ∆ ⎜ ⎟ Base( ⎝ ⎠ ⎛ ⎞ Amount( ⎜ ⎟ ⎜ ⎟ Total( ⎝ ⎠ Interest = number of compounding periods. = periodic interest rate, expressed as a decimal. = present value.
  • Page 186: Compound Interest

    186 Appendix D: Formulas Used Compound Interest Without an odd period: ⎡ − ⎤ − − ⋅ ⋅ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ With simple interest used for an odd period: ⎡ − ⎤ INTG( − ⎢ ⎥ FRAC( ⎢...
  • Page 187: Discounted Cash Flow Analysis

    Appendix D: Formulas Used Discounted Cash Flow Analysis Net Present Value = net present value of a discounted cash flow. = cash flow at period j. Internal Rate of Return = number of cash flows = cash flow at period j. = Internal Rate of Return ⎡...
  • Page 188: Bonds

    188 Appendix D: Formulas Used Bonds Reference: Spence, Graudenz, and Lynch, Standard Securities Calculation Methods, Securities Industry Association, New York, 1973. = days between issue date and maturity date. = days between settlement date and maturity date. = days between beginning of current coupon period and settlement date.
  • Page 189: Depreciation

    Appendix D: Formulas Used Depreciation = asset’s useful life expectancy. = starting book value. = salvage value. FACT = declining-balance factor expressed as a percentage. = period number. = depreciation expense during period j. = remaining depreciable value at end of period j = RDV –...
  • Page 190: Declining-balance Depreciation

    190 Appendix D: Formulas Used Program for partial year: ⎛ ⎞ ⎛ ⎞ ⋅ ⎟ ⋅ ⎟ − ⎜ ⎜ ⎝ ⎠ ⎝ ⎠ SOYD ⎛ ⎞ − LADJ ⎜ ⋅ ⎟ ⎟ − − ≠ for j ⎜ SOYD ⎝...
  • Page 191: Interest Rate Conversions

    Appendix D: Formulas Used Interest Rate Conversions = number of compounding periods per year. = the effective annual interest rate as a decimal. = the nominal annual interest rate as a decimal. Finite Compounding ⎛ ⎞ − ⎜ ⎟ ⎝ ⎠...
  • Page 192: Standard Deviation

    192 Appendix D: Formulas Used ∑ ∑ ⋅ ⎡ ⎤ ∑ − ⎢ ⎥ ⎣ ⎦ ⎡ ⎤ ⎡ ⎤ ∑ ∑ ∑ ∑ − ⋅ − ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ Standard Deviation ∑...
  • Page 193: Appendix E: Battery, Warranty, And Service Information

    Service Information Battery The hp 12c is shipped with one 3 Volt CR2023 Lithium battery. Battery life depends on how the calculator is used. If the calculator is being used to perform operations other than running programs, it uses much less power.
  • Page 194: Verifying Proper Operation (self-tests)

    ve been los s been res for any rea to turn o ou do so, th Be careful n ote: . Replace t ay be lost ( 194 Appendix E: Battery, Warranty, and Service Information d off, slide the battery cover off. To install a new battery, use the following procedure: h positive polarity facing outward.
  • Page 195 Service (Page 197). The status indicators turned on at the end of this test include some that normally are not displayed on the hp 12c. † If the calculator displays Error 9 as a result of the ;/µ test or the ;/+ test but you wish to continue using your calculator, you should reset Continuous Memory as described on page 70.
  • Page 196: Warranty

    196 Appendix E: Battery, Warranty, and Service Information Warranty hp 12c Financial Calculator; Warranty period: 12 months 1. HP warrants to you, the end-user customer, that HP hardware, accessories and supplies will be free from defects in materials and workmanship after the date of purchase, for the period specified above.
  • Page 197: Service

    Appendix E: Battery, Warranty, and Service Information Some countries, States or provinces do not allow the exclusion or limitation of incidental or consequential damages, so the above limitation or exclusion may not apply to you. 8. The only warranties for HP products and services are set forth in the express warranty statements accompanying such products and services.
  • Page 198 198 Appendix E: Battery, Warranty, and Service Information Asia Pacific Country : Telephone numbers Australia +61-3-9841-5211 Singapore +61-3-9841-5211 L.America Country : Telephone numbers Argentina 0-810-555-5520 Brazil Sao Paulo 3747-7799; ROTC 0-800-157751 Mexico Mx City 5258-9922; ROTC 01-800-472-6684 Venezuela 0800-4746-8368 Chile 800-360999 Columbia 9-800-114726...
  • Page 199: Regulatory Information

    Appendix E: Battery, Warranty, and Service Information Regulatory Information This section contains information that shows how the hp 12c financial calculator complies with regulations in certain regions. Any modifications to the calculator not expressly approved by Hewlett-Packard could void the authority to operate the 12c in these regions.
  • Page 200: Disposal Of Waste Equipment By Users In Private Household In The European Union

    200 Appendix E: Battery, Warranty, and Service Information Disposal of Waste Equipment by Users in Private Household in the European Union This symbol on the product or on its packaging indicates that this product must not be disposed of with your other household waste. Instead, it is your responsibility to dispose of your waste equipment by handing it over to a designated collection point for the recycling of waste electrical and electronic equipment.
  • Page 201: Appendix F: United Kingdom Calculations

    Appendix F United Kingdom Calculations 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 earlier in this handbook. Certain problems, however, require different calculation methods in the United Kingdom than in the United States, even though the terminology describing the problems may be similar.
  • Page 202: Annual Percentage Rate (apr) Calculations

    202 Appendix F: United Kingdom Calculations Annual Percentage Rate (APR) Calculations In the United Kingdom, the calculation of the Annual Percentage Rate of Charge (APR) in accordance with the United Kingdom Consumer Credit Act (1974) differs from the calculation of the APR in the United States. Unlike the practice in the United States, where the APR can be calculated by multiplying the periodic interest rate by the number of periods per year, in the United Kingdom the APR is calculated by converting the periodic interest rate to the “effective annual rate,”...
  • Page 203: Function Key Index

    Function Key Index 0 —9 digits. Used CLEAR H Clears General for keying in numbers contents of stack (X,Y,Z ; Power on /off key (page 19) and display and T), all storage (page 16). formatting (page 71). registers, statistical registers, and financial f Shift key.
  • Page 204 204 Function Key Index M Stores or computes V Calculates Financial future value (final cash depreciation using CLEAR G Clears flow) of a financial straight-line method. contents of financial problem (page 32). (page 68). registers (page 33). ! Amortizes x E Calculates bond ×...
  • Page 205 Function Key Index Ö Computes mean Mathematics Number Alteration (average) of x-values and r Computes square root B Rounds mantissa of y-values using of number in displayed 10digit number in accumulated statistics X-register (page 83). X-register to match the (page 77). display (page 83).
  • Page 206: Programming Key Index

    Programming Key Index s Program/Run. Toggles into and out of Program mode. Automatically sets program to line 00 when returning to Run mode (page 86). N Memory map. Describes the current allocation of memory; the number of lines allotted to program memory and the number of available data registers (page 93).
  • Page 207 Programming Key Index Program Mode Run Mode Active Keys: Pressed from Executed as a keyboard: recorded program instruction: t Run/Stop. Begins execution of a stored t Run/Stop. Stops program. Stops program execution execution if program is (page 101). running (page 89). i Go to.
  • Page 208: Subject Index

    Subject Index Bonds, municipal, 67 Bonds, state and local government, , 12, 54, 172 Bonds, U.S. Treasury, 66 Adding instructions, 114–19 Branching, 103–12, 116 Advance payments, 151, 156 Branching, adding instructions by, Amortization, 38, 54–56, 186 116–19 Annual interest rate, 39 Branching, conditional, 107–8 Annual Percentage Rate, 52–53, Branching, simple, 103...
  • Page 209 Subject Index Compound interest, 39–53, 186 Display format, mantissa, 73 Compound interest calculation, 11 Display format, standard, 71 Compounding periods, 34, 39 Display formats, number, 71 Conditional branching, 107–8 Display, scientific notation, 72 Conditional test instructions, 107 Displaying numbers, 32 Constants, arithmetic calculations Displays, special, 73 with, 177...
  • Page 210 210 Subject Index Interest, simple, 33 Number display formats, 71 Internal rate of return, 57 Numbers, keying in, 17 Internal rate of return, calculating, Numbers, large, 18 Numbers, negative, 17 Internal rate of return, modified, 148 Numbers, recalling, 23 Interrupting a program, 97 Numbers, storing, 23 IRR, 57, 148 Odd-period calculations, 50...
  • Page 211 Subject Index Program, running one line at a time, Square Root, 83 Stack, 170 Program, stopping, 97, 101 Standard deviation, 79 Program, storing, 120 Statistics, 76 Programming, 88 Status indicators, 71 Programs, multiple, 120 Storage register arithmetic, 24 PV, 36 Storage registers, clearing, 24 Storing numbers, 32 Storing programs, 120...

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