HP 12C Platinum Owner’s Handbook and Problem-Solving Guide © Hewlett-Packard Company 2003
Introduction About This Handbook This HP 12C Platinum Owner’s Handbook and Problem-Solving Guide is intended to help you get the most out of your investment in your HP 12C Platinum Programmable Financial Calculator. Although the excitement of acquiring this powerful financial tool may prompt you to set this handbook aside and immediately begin “pressing buttons,” in the long run you’ll profit by reading through this handbook and working through the examples it contains.
Introduction 3 z The various appendices describe additional details of calculator operation as well as warranty and service information.
Contents Introduction ...................................................................................... 2 About This Handbook ..................................................................................... 2 Financial Calculations in the United Kingdom ................................................ 3 For More Solutions to Financial Problems...................................................... 3 Part I: Problem Solving................................................
Contents Compound Interest Calculations .................................................................. Specifying the Number of Compounding Periods and the Periodic Interest Rate ........................................................................................... Calculating the Number of Payments or Compounding Periods ............ Calculating the Periodic and Annual Interest Rates ............................... Calculating the Present Value .................................................
Contents 7 Part II: Programming....................................................85 Section 8: Programming Basics........................................................ 86 Why Use Programs? .................................................................................... Creating a Program ...................................................................................... Running a Program ...................................................................................... Program Memory.......
Contents Section 14: Leasing ............................................................................ 148 Advance Payments..................................................................................... Solving For Payment ............................................................................ Solving for Yield.................................................................................... Advance Payments With Residual .............................................................
Contents Error 4: Memory.......................................................................................... Error 5: Compound Interest ........................................................................ Error 6: Storage Registers.......................................................................... Error 7: IRR ................................................................................................ Error 8: Calendar ...................................................................
Contents Appendix G: United Kingdom Calculations ................................ 203 Mortgages................................................................................................... 203 Annual Percentage Rate (APR) Calculations ............................................. 203 Bond Calculations....................................................................................... 204 Function Key Index .....................................................................
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.
Making Financial Calculations Easy time to produce an answer. (This is typically just a few seconds, but the ¼, !, L, and S functions could require a half-minute or more.) During these calculations, the word running flashes in the display to let you know that the calculator is running. Keystrokes Display fCLEARHf2 0.00 4gA 48.00 6gC 0.50 500P g× $ 500.00 500.00 –21,396.61 a Clears previous data inside the calculator and sets display to show two decimal places.
Making Financial Calculations Easy Keystrokes Display fCLEARG 10,470.85 14gA 168.00 6gC 0.50 10925.76M g P 10.925.76 10.925.76 –41.65 13 Clears previous financial data inside the calculator. Calculates and stores the number of compounding periods. Calculates and stores the periodic interest rate. Stores the future value required. Sets payment mode to End. Monthly payment required.
Part I Problem Solving
Section 1 Getting Started Power On and Off To begin using your HP 12C Platinum, press the ; key1. Pressing ; again turns the calculator off. If not manually turned off, the calculator will turn off automatically 8 to 17 minutes after it was last used. Low-Power Indication A battery symbol ( ) shown in the upper-left corner of the display when the calculator is on signifies that the available battery power is nearly exhausted. To replace the batteries, refer to Appendix F.
Section 1: Getting Started 17 appropriate prefix key (for example, “Pressing fL …”). References to the functions shown on the keyboard in gold under the bracket labeled “CLEAR” appear throughout this handbook preceded by the word “CLEAR” (for example, “The CLEAR H function …” or “Pressing fCLEARH …”). If you press the f or g prefix key mistakenly, you can cancel it by pressing fCLEAR X. This can also be pressed to cancel the ?, :, and i keys.
Section 1: Getting Started Keying in Large Numbers Since the display cannot show more than 10 digits of a number, numbers greater than 9,999,999,999 cannot be entered into the display by keying in all the digits in the number. However, such numbers can be easily entered into the display if the number is expressed in a mathematical shorthand called “scientific notation.” To convert a number into scientific notation, move the decimal point until there is only one digit (a nonzero digit) to its left.
Section 1: Getting Started 19 The RPN and ALG Keys The calculator can be set to perform arithmetic operations in either RPN (Reverse Polish Notation) or ALG (Algebraic) mode. In reverse polish notation (RPN) mode, the intermediate results of calculations are stored automatically, hence you do not have to use parentheses. In algebraic (ALG) mode, you perform addition, subtraction, multiplication, and division in the traditional way. To select RPN mode: Press f] to set the calculator to RPN mode.
Section 1: Getting Started In summary, to perform an arithmetic operation: 1. Key in the first number. 2. Press \ to separate the second number from the first. 3. Key in the second number. 4. Press +,-,§, or z to perform the desired operation. For example to calculate 13 ÷ 2, proceed as follows: Keystrokes (RPN mode) Display 13 13. \ 13.00 2 2. z 6.50 Keys the first number into the calculator. Pressing \ separates the second number from the first. Keys the second number into the calculator.
Section 1: Getting Started 21 Example: Suppose you’ve written three checks without updating your checkbook, and you’ve just deposited your paycheck for $1,053.00 into your checking account. If your latest balance was $58.33 and the checks were written for $22.95, $13.70, and $10.14, what is the new balance? Solution: When written down on paper, this problem would read 58.33 – 22.95 – 13.70 – 10.14 + 1053 Keystrokes (RPN mode) Display 58.33 \ 58.33 58.33 22.95 - 22.95 35.38 13.70 13.70 - 21.68 10.
Section 1: Getting Started The preceding example demonstrates how the HP 12C Platinum calculates just as you would using pencil and paper (except a lot faster!): ... and you see the results of each operation immediately. You do one operation at a time ... Let’s see this happening in a different type of calculation – one that involves multiplying groups of two numbers and then adding the results.
Section 1: Getting Started 23 proper time, just as you would yourself.2 But with the HP 12C Platinum, you don’t need to write down the results of an intermediate calculation, and you don’t even need to manually store it and recall it later. By the way, notice that in step 2 you needed to press \ again. This is simply because you were again keying in two numbers immediately following each other, without performing a calculation in between.
Section 1: Getting Started Storing and Recalling Numbers To store the number from the display into a data storage register: 1. Press ? (store). 2. Key in the register number: 0 through 9 for registers 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.
Section 1: Getting Started 25 Clearing Storage Registers To clear a single storage register – that is, to replace the number in it with zero – merely store zero into it. You need not clear a storage register before storing data into it; the storing operation automatically clears the register before the data is stored. To clear all storage registers at once – including the financial registers, the stack registers, and the LAST X register – press fCLEARH.3 This also clears the display.
Section 1: Getting Started Keystrokes Display 58.33?0 58.33 Stores the current balance in register R0. 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. 13.70?-0 10.14?-0 1053?+0 :0 13.70 10.14 1,053.00 1,064.54 Subtracts the second check. Subtracts the third check. Adds the deposit. Recalls the number in R0 to check the new balance.
Section 2 Percentage and Calendar Functions Percentage Functions The HP 12C Platinum includes three keys for solving percentage problems: b, à, and Z. You don’t need to convert percentages to their decimal equivalents; this is done automatically when you press any of these keys. Thus, 4% need not be changed to 0.04; you key it in the way you see and say it: 4b. Percentages In RPN mode, to find the amount corresponding to a percentage of a number: 1. Key in the base number. 2. Press \. 3.
Section 2: Percentage and Calendar Functions the base amount inside after you calculate a percentage amount. To calculate a net amount, simply calculate the percentage amount, then press = or -. Example: You’re buying a new car that lists for $13,250. The dealer offers you a discount of 8%, and the sales tax is 6%. Find the amount the dealer is charging you, then find the total cost to you, including tax. Keystrokes (RPN mode) Display 13250\ 8b 6b = 13,250.
Section 2: Percentage and Calendar Functions 29 the percent difference is called the markup; if the base number entered is the retail cost, the percent difference is called the margin. Examples of markup and margin calculations are included in the HP 12C Platinum Solutions Handbook. Percent of Total In RPN mode, to calculate what percentage one number is of another: 1. Calculate the total amount by adding the individual amounts, just as in a chain arithmetic calculation. 2.
Section 2: Percentage and Calendar Functions To find what percentage a number is of a total, when you already know the total number 1. Key in the total number. 2. Press \ to separate the other number from the total number. 3. Key in the number whose percentage equivalent you wish to find. 4. Press Z. For example, if you already knew in the preceding example that the total sales were $7.95 million and you wanted to find what percentage of that total occurred in Europe: Keystrokes Display 7.95\ 7.
Section 2: Percentage and Calendar Functions 31 For example, to key in April 7, 2003: Keystrokes Display 4.072003 4.072003 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, 2003: Keystrokes Display 7.042003 7.
Section 2: Percentage and Calendar Functions Example: If you purchased a 120-day option on a piece of land on 14 May 2003, what would be the expiration date? Assume that you normally express dates in the day-month-year format. Keystrokes Display gÔ 7.04 14.052003\ 14.05 120gD 11,09,2003 4 Sets date format to day-monthyear. (Display shown assumes date remains from preceding example.
Section 2: Percentage and Calendar Functions Keystrokes Display gÕ 11.09 6.032003\ 6.03 10.152004gÒ 500.00 ~ 492.00 33 Sets date format to month-day-year. (Display shown assumes date remains from preceding example.) Keys in earlier date and separates it from the later date. Keys in later date. Display shows actual number of days. Number of days counted on the basis of a 30-day month.
Section 3 Basic Financial Functions The Financial Registers In addition to the data storage registers discussed on page 23, the HP 12C Platinum has five special registers in which numbers are stored for financial calculations. These registers are designated n, i, PV, PMT, and FV.
Section 3: Basic Financial Functions 35 The financial registers are also cleared when you press fCLEARH and when Continuous Memory is reset (as described on page 70). Simple Interest Calculations The HP 12C Platinum simultaneously calculates simple interest on both a 360day basis and a 365-day basis. You can display either one, as described below. Furthermore, with the accrued interest in the display, you can calculate the total amount (principal plus accrued interest) by pressing +. 1.
Section 3: Basic Financial Functions basis. What is the amount of accrued interest he will owe you in 60 days, and what is the total amount owed? Keystrokes (RPN mode) Display 60n 7¼ 450Þ$ 60.00 7.00 –450.00 fÏd~ 5.18 + 455.18 If you have not altered the numbers in the n, i, and PV registers since the preceding example, you may skip these keystrokes. Accrued interest, 365-day basis. Total amount: principal plus accrued interest.
Section 3: Basic Financial Functions 37 Suppose you deposited (paid out) $1,000 into an account that pays 6% annual interest and is compounded monthly, and you subsequently deposited an additional $50 at the end of each month for the next 2 years. The cash flow diagram describing the problem would look like this: The arrow pointing up at the right of the diagram indicates that money is received at the end of the transaction.
Section 3: Basic Financial Functions z i is the interest rate per compounding period. The interest rate shown in the cash flow diagram and entered into the calculator is determined by dividing the annual interest rate by the number of compounding periods. In the problem illustrated above, i = 6% ÷ 12. z PV – the present value – is the initial cash flow or the present value of a series of future cash flows. In the problem illustrated above, PV is the $1,000 initial deposit.
Section 3: Basic Financial Functions 39 payments in advance yield different results than calculations involving payments in arrears. Illustrated below are portions of cash flow diagrams showing payments in advance (Begin) and payments in arrears (End). In the problem illustrated in the cash flow diagram above, payments are made in arrears. Begin End 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.
Section 3: Basic Financial Functions
Section 3: Basic Financial Functions 41 Compound Interest Calculations Specifying the Number of Compounding Periods and the Periodic Interest Rate Interest rates are usually quoted at the annual rate (also called the nominal rate): that is, the interest rate per year. However, in compound interest problems, the interest rate entered into i must always be expressed in terms of the basic compounding period, which may be years, months, days, or any other time unit.
Section 3: Basic Financial Functions If the answer calculated is not an integer (that is, there would be nonzero digits to the right of the decimal point), the calculator rounds the answer up to the next higher integer before storing it in the n register and displaying it.8 For example, if n were calculated as 318.15, 319.00 would be the displayed answer. n is rounded up by the calculator to show the total number of payments needed: n–1 equal, full payments, and one final, smaller payment.
Section 3: Basic Financial Functions 43 Because the calculator rounds the calculated value of n up to the next higher integer, in the preceding example it is likely that – while 328 payments will be required to pay off the loan – only 327 full payments of $325 will be required, the next and final payment being less than $325. You can calculate the final, fractional, 328th payment as follows: Keystrokes (RPN mode) Display 328n M 328.00 181.89 :P + –325.00 –143.11 a Stores total number of payments.
Section 3: Basic Financial Functions Keystrokes (RPN mode) Display fCLEARG 6.25\24z¼ 775Þ$ 0.26 Calculates and stores i. –775.00 50ÞP –50.00 4000M g n 2z 4,000.00 4,000.00 58.00 29.00 Stores PV (with minus sign for cash paid out). Stores PMT (with minus sign for cash paid out). Stores FV. Sets the payment mode to End. Number of semimonthly deposits. Number of months. As in Example 1, it is likely that only 57 full deposits will be required, the next and final deposit being less than $50.
Section 3: Basic Financial Functions 45 In this example, M must be pressed twice, since the preceding key pressed was z. If we had stored the number of deposits in n (as we did following Example 1), we would have to press M only once here, since the preceding key pressed would have been w (as it was following Example 1). Remember that it is not necessary to store the number of payments in n before calculating the amount of the final, fractional payment. (Refer to the preceding footnote.
Section 3: Basic Financial Functions Keystrokes (RPN mode) Display fCLEARG 8\4§n 6000Þ$ 10000M ¼ 4§ 32.00 Calculates and stores n. –6,000.00 Stores PV (with minus sign for cash paid out). 10,000.00 Stores FV. Periodic (quarterly) interest rate. 1.61 Annual interest rate. 6.44 Calculating the Present Value 1. Press fCLEARG to clear the financial registers. 2. Enter the number of payments or periods, using n or A. 3. Enter the periodic interest rate, using ¼ or C. 4.
Section 3: Basic Financial Functions Keystrokes Display fCLEARG 4gA 15gC 150ÞP 48.00 Calculates and stores n. 1.25 –150.00 g $ 1500+ –150.00 5,389.72 6,889.72 Calculates and stores i. Stores PMT (with minus sign for cash paid out). Sets payment mode to End. Maximum amount of loan. Maximum purchase price. 47 Example 2: A development company would like to purchase a group of condominiums with an annual net cash flow of $17,500.
Section 3: Basic Financial Functions Calculating the Payment Amount 1. Press fCLEARG to clear the financial registers. 2. Enter the number of payments or periods, using n or A. 3. Enter the periodic interest rate, using ¼ or C. 4. Enter either or both of the following: z Present value, using $. z Future value, using M. Note: Remember to observe the cash flow sign convention. 5. Press g× or g to set the payment mode. 6. Press P to calculate the payment amount.
Section 3: Basic Financial Functions Keystrokes Display fCLEARG 15\2§n 9.75\2z¼ 3200Þ$ 30.00 4.88 –3200.00 60000M g P 60,000.00 60,000.00 –717.44 49 Calculates and stores n. Calculates and stores i. Stores PV (with minus sign for cash paid out). Stores FV. Sets payment mode to End. Semiannual payment (with minus sign for cash paid out). 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.
Section 3: Basic Financial Functions Example 1: In Example 1 on page 48, we calculated that the payment amount on a 29-year, $43,400 mortgage at 14¼% annual interest is $523.99. If the seller requests a balloon payment at the end of 5 years, what would be the amount of the balloon? Keystrokes Display fCLEARG 5gA 14.25gC 43400$ 523.99ÞP 60.00 1.19 43,400.00 –523.99 g M Calculates and stores n. Calculates and stores i. Stores PV. Stores PMT (with minus sign for cash paid out).
Section 3: Basic Financial Functions Keystrokes Display fCLEARG 2gA 6.25gC 50ÞP 24.00 Calculates and stores n. 0.52 –50.00 g× M –50.00 1,281.34 Calculates and stores i. Stores PMT (with minus sign for cash paid out). Sets payment mode to Begin. Balance after 2 years. 51 Example 3: Property values in an unattractive area are depreciating at the rate of 2% per year. Assuming this trend continues, calculate the value in 6 years of property presently appraised at $32,000.
Section 3: Basic Financial Functions period” or the “odd days”. (Note that the odd period is always assumed by the calculator to occur before the first full payment period.) The following two cash flow diagrams represent transactions including an odd period for payments in advance (Begin) and for payments in arrears (End). . Begin odd period End odd period You can calculate i, PV, PMT, and FV for transactions involving an odd period simply by entering a noninteger n.
Section 3: Basic Financial Functions 53 must be divided by the number of days in a period. If interest is compounded monthly, for this number you can use either 30, 365/12, or (if the odd period falls entirely within a single month) the actual number of days in that month. Usually, a monthly period is taken to be 30 days long. At your option, the calculations of i, PV, PMT, and FV can be performed with either simple interest or compound interest accruing during the odd period.
Section 3: Basic Financial Functions Example 2: A 42-month car loan for $3,950 began accruing interest on July 19, 2003, so that the first period began on August 1, 2003. Payments of $120 are made at the end of each month. Calculate the annual percentage rate (APR), using the actual number of odd days and simple interest for the odd period. Keystrokes (RPN mode) Display fCLEARG ?Æ 7.192003\ 7.19 8.012003 8.012003 gÒ 30z 13.00 0.43 42+n 42.43 3950$ 120ÞP 3,950.00 –120.00 ¼ 12§ 1.16 13.
Section 3: Basic Financial Functions 55 To obtain an amortization schedule: 1. Press fCLEARG to clear the financial registers. 2. Enter the periodic interest rate, using ¼ or C. 3. Enter the amount of the loan (the principal), using $. 4. Key in the periodic payment, then press ÞP (the sign of PMT must be negative, in accordance with the cash flow sign convention). 5. Press g× or (for most direct reduction loans) g to set the payment mode. 6. Key in the number of payments to be amortized. 7.
Section 3: Basic Financial Functions The number of payments keyed in just before f! is pressed is taken to be the payments following any that have already been amortized. Thus, if you now press 12f!, your HP 12C Platinum will calculate the amounts applied to interest and to the principal from the second year’s payments (that is, the second 12 months): Keystrokes Display 12f! –6,570.72 Portion of second year’s payments applied to interest. Portion of second year’s payments –309.
Section 3: Basic Financial Functions 57 If you want to generate an amortization schedule but do not already know the monthly payment: 1. Calculate PMT as described on page 48. 2. Press 0n to reset n to zero. 3. Proceed with the amortization procedure listed on page 55 beginning with step 6. Example: Suppose you obtained a 30-year mortgage instead of a 25-year mortgage for the same principal ($50,000) and at the same interest rate (13¼%) as in the preceding example.
Section 4 Additional Financial Functions Discounted Cash Flow Analysis: NPV and IRR The HP 12C Platinum provides functions for the two most widely-used methods of discounted cash flow analysis: l (net present value) and L (internal rate of return). These functions enable you to analyze financial problems involving cash flows (money paid out or received) occurring at regular intervals.
Section 4: Additional Financial Functions 59 A comparison of the NPV’s of alternative investment possibilities indicates which of them is most desirable: the greater the NPV, the greater the increase in the financial value of the investor’s assets. IRR is the rate of return at which the discounted future cash flows equal the initial cash outlay: IRR is the discount rate at which NPV is zero.
Section 4: Additional Financial Functions 2. Key in the amount of the initial investment, press Þ if that cash flow is negative, then press gJ. If there is no initial investment, press 0 gJ. 3. Key in the amount of the next cash flow, press Þ if the cash flow is negative, then press gK. If the cash flow amount is zero in the next period, press 0 gK. 4. Repeat step 3 for each cash flow until all have been entered.
Section 4: Additional Financial Functions Keystrokes (Cont.) Display 4500gK 5500gK 130000gK :n 4,500.00 5,500.00 4,500.00 130,000.00 5.00 13¼ fl 13.00 212.18 4500gK 61 Stores CF2. Stores CF3. Stores CF4. Stores CF5. Checks number of cash flow amounts entered (in addition to CF0. Stores i. NPV. Since NPV is positive, the investment would increase the financial value of the investor’s assets. Calculating NPV for Grouped Cash Flows.
Section 4: Additional Financial Functions 3. If the initial investment consists of more than one cash flow of the amount entered in step 2, key in the number of those cash flows, then press ga. If ga is not pressed, the calculator assumes that N0 is 1. 4. Key in the amount of the next cash flow, press Þ if that cash flow is negative, then press gK. If the cash flow amount is zero in the next period, press 0gK. 5.
Section 4: Additional Financial Functions Keystrokes Display 3ga 3.00 9100gK 9000gK 2ga 4500gK 100000gK :n 13.5¼ fl 63 Number of times this cash flow amount occurs consecutively. Next cash flow amount. 9,100.00 Next cash flow amount. 9,000.00 Number of times this cash flow 2.00 amount occurs consecutively. Next cash flow amount. 4,500.00 100,000.00 Final cash flow amount. Seven different cash flow amounts 7.00 have been entered. Stores i. 13.50 NPV 907.
Section 4: Additional Financial Functions finding IRR are extremely complex, involving a series of iterations – that is, a series of successive calculations. In each iteration, the calculator uses an estimate of IRR as the interest rate in a computation of NPV. The iterations are repeated until the computed NPV reaches about zero.16 If you do not want to wait for the computation of IRR to be completed, press any key.
Section 4: Additional Financial Functions 65 Note: Neither L nor l change the number in the n register. However, each time :gK is pressed, the number in the n register is decreased by 1. If this is done, or if you manually change the number in the n register in order to display a single Nj and/or CFj, be sure to reset the number in the n register to the total number of cash flow amounts originally entered (not including the amount of the initial investment CF0).
Section 4: Additional Financial Functions Changing Cash Flow Entries To change a cash flow amount: z 1. Key the amount into the display. 2. Press ?. 3. Key in the number of the register containing the cash flow amount to be changed. To change the number of times a cash flow amount occurs consecutively – that is, to change the Nj for a CFj: z 1. Store the number of that cash flow amount (that is, j) in the n register. 2.
Section 4: Additional Financial Functions 67 Bond Calculations The HP 12C Platinum enables you to solve for bond price (and the interest accrued since the last interest date) and the yield to maturity.19 The E and S calculations are done assuming a semiannual coupon payment and using an actual/actual basis (such as for U.S. Treasury bonds and U.S. Treasury notes). In accordance with market convention, prices are based on a redemption (par) value of 100.
Section 4: Additional Financial Functions Bond Yield 1. Enter the quoted price (as a percent of par), using $. 2. Enter the annual coupon rate (as a percentage), using P. 3. Key in the settlement (purchase) date, then press \. 4. Key in the maturity (redemption) date. 5. Press fS. The yield to maturity is shown in the display and also is stored in the i register. Note: Remember that the S function may take a significant amount of time to produce an answer, during which the calculator displays running.
Section 4: Additional Financial Functions 69 6. Press: z fV for depreciation using the straight-line method. z fÝ for depreciation using the sum-of-the-years digits method. z f# for depreciation using the declining-balance method. V, Ý, and # each place the amount of depreciation in the display. To display the remaining depreciable value (the book value less the salvage value) after the depreciation has been calculated, press ~.
Section 5: 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.
Section 5: Additional Operating Features 71 Number Display Formats When the calculator is first turned on after coming from the factory or after Continuous Memory has been reset, answers are displayed with two decimal places. Keystrokes (RPN mode) Display 19.8745632\ 5- 19.87 14.87 Although you see only two decimal places, all calculations in your HP 12C Platinum are performed with full 10-digit numbers. Yo u s e e o n l y these digits ... . . .
Section 5: Additional Operating Features Keystrokes Display f4 f1 f0 f9 14.8746 14.9 15. 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; they are not reset each time the calculator is turned on.
Section 5: Additional Operating Features 73 To set the display format to scientific notation, press f.. For example (assuming the display still shows 14.87456320 from the preceding example): Keystrokes Display f. 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.
Section 5: Additional Operating Features If a calculation results in a number whose magnitude is less than 10-99, the calculation is not halted, but the value 0 is used for that number in subsequent calculations. Errors. If you attempt an improper operation – such as division by zero – the calculator will display the word Error followed by a digit (0 through 9). To clear the Error display, press any key.
Section 5: Additional Operating Features 75 Arithmetic Calculations With Constants Example: At Permex Pipes a certain pipe fitting is packaged in quantities of 15, 75, and 250. If the cost per fitting is $4.38, calculate the cost of each package. Keystrokes (RPN mode) Display 15\ 4.38 § 75 gF 15.00 4.38 65.70 75. 4.38 § 250 gF § 328.50 250. 4.38 1,095.00 Keys first quantity into calculator. Keys unit cost into display. Cost of a package of 15. Keys second quantity into display.
Section 6 Statistics Functions Accumulating Statistics The HP 12C Platinum can perform one- or two-variable statistical calculations. The data is entered into the calculator using the _ key, which automatically calculates and stores statistics of the data into storage registers R1, through R6. (These registers are therefore referred to as the “statistics registers.”) Before beginning to accumulate statistics for a new set of data, you should clear the statistics registers by pressing fCLEAR².
Section 6: Statistics Functions Register Statistic R1 (and display) n: number of data pairs accumulated. R2 Σx: summation of x-values. R3 Σx2: summation of squares of x-values. R4 Σy: summation of y-values. R5 Σy2 summation of squares of y-values. R6 Σxy: summation of products of x-values and y-values.
Section 6: Statistics Functions Salesperson Hours/Week Hours/Week 1 32 $17,000 2 40 $25,000 3 45 $26,000 4 40 $20,000 5 38 $21,000 6 50 $28,000 7 35 $15,000 To find the average workweek and sales of this sample: Keystrokes Display fCLEAR² 32\ 17000_ 40\ 25000_ 45\ 26000_ 40\ 20000_ 38\ 21000_ 50\ 28000_ 35\ 15000_ 00.00 32.00 1.00 40.00 2.00 45.00 3.00 40.00 4.00 38.00 5.00 50.00 6.00 35.00 7.00 gÖ 21,714.29 Total number of entries in the sample.
Section 6: Statistics Functions 79 Example: To calculate the standard deviations of the x-values and of the y-values from the preceding example: Keystrokes Display gv ~ 4,820.59 6.03 Standard deviation of sales. Standard deviation of hours worked. The formulas used in the HP 12C Platinum for calculating sx, and sy give best estimates of the population standard deviation based on a sample of the population. Thus, current statistical convention calls them sample standard deviations.
Section 6: Statistics Functions Example: Using the accumulated statistics from the preceding problem, estimate the amount of sales delivered by a new salesperson working 48 hours per week. Keystrokes Display 48gQ 28,818.93 Estimated sales for a 48 hour workweek. The reliability of a linear estimate depends upon how closely the data pairs would, if plotted on a graph, lie in a straight line. The usual measure of this reliability is the correlation coefficient, r.
Section 6: Statistics Functions 81 Weighted Mean You can compute the weighted mean of a set of numbers if you know the corresponding weights of the items in question. 1. Press fCLEAR². 2. Key in the value of the item and press \, then key in its weight and press _. Key in the second item’s value, press \, key in the second weight, and press _. Continue until you have entered all the values of the items and their corresponding weights. The rule for entering the data is “item \ weight _.” 3.
Section 7 Mathematics and Number-Alteration Functions The HP 12C Platinum provides several keys for mathematical functions and for altering, numbers. These functions are useful for specialized financial calculations as well as for general mathematics calculations. One-Number Functions Most of the mathematics functions require that only one number be in the calculator (that is, the number in the display) before the function key is pressed.
Section 7: Mathematics and Number-Alteration Functions 83 Integer. Pressing gÑ replaces the number in the display by its integer portion – that is, it replaces each digit to the right of the decimal point by 0. The number is changed inside the calculator as well as in the display. The original number can be recalled to the display by pressing gF. Fractional. Pressing gT replaces the number in the display by its fractional portion – that is, it replaces all digits to the left of the decimal point by 0.
Section 7: Mathematics and Number-Alteration Functions The Power Function Pressing q calculates a power of a number – that is, yx. Like the arithmetic function +, q requires two numbers: 1. Key in the base number (which is designated by the y on the key). 2. Press \ to separate the second number (the exponent) from the first (the base). 3. Key in the exponent (which is designated by the x on the key). 4. Press q to calculate the power. To Calculate Keystrokes (RPN mode) Display 21.4 2\1.4q 2.
Part II Programming
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.
Section 8: Programming Basics 87 Keystrokes (RPN mode) Display 200 \ 200. 200.00 25b 5 + 50.00 150.00 5. 155.00 Keys in cost of item. Separates cost of item from percentage to be keyed in next. Amount of discount. Price less discount. Handling charge. Net cost (price less discount plus handling charge). Next, set the calculator to Program mode and erase any program(s) already stored: Keystrokes (RPN mode) Display fs fCLEARÎ 000, 000, Sets calculator to Program mode. Clears program(s).
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 (RPN mode) Display fs 155.00 f] 625 t 159 t 155.00 625. 473.75 159. 124.25 Sets calculator to Run mode. Display shows number previously calculated. Sets RPN mode. Keys in price of typewriter. Net cost of typewriter. Keys in list price of chair. Net cost of chair.
Section 8: Programming Basics 89 Identifying Instructions in Program Lines Each key on the HP 12C Platinum keyboard – except for the digit keys 0 through 9 – is identified by a two-digit “keycode” that corresponds to the key’s position on the keyboard.
Section 8: Programming Basics Displaying Program Lines Pressing fs to set the calculator from Run mode to Program mode displays the line number and keycode for the program line to which the calculator is currently set. Occasionally you’ll want to check several or all of the instructions stored in program memory.
Section 8: Programming Basics 91 Program line 007 contains the last instruction you keyed into program memory. However, if you press Ê again, you’ll see that this is not the last line stored in program memory: Keystrokes Display 008,43,33,000 Program line 008 As you should now be able to tell from the keycodes displayed, the instruction in program line 008 is gi000.
Section 8: Programming Basics program memory consists of 8 program lines, and there are 20 storage registers available for storage of data. As you key in a 310th instruction, storage register R0.9 is automatically converted into seven new lines of program memory. The instruction you key in is stored in program line 310, and the instruction i000 is automatically stored in program lines 311 through 316.
Section 8: Programming Basics 93 To determine at any time how many program lines (including those containing i000) are currently in program memory and how many storage registers are currently available for conversion to program lines or for data storage, press gN (memory). The calculator will respond with a display like the following: Up to 400 instructions can be stored in program memory.
Section 8: Programming Basics For example, assuming the calculator is still in Program mode, you can set it to program line 000 as follows: Keystrokes Display gi.000 000, Program line 000 Executing a Program One Line at a Time Pressing Ê repeatedly with the calculator in Program mode (as described earlier) enables you to verify that the program you have stored is identical to the program you wrote – that is, to verify that you have keyed the instructions in correctly.
Section 8: Programming Basics Keystrokes (RPN mode) 95 Display 156.25 Ê 005, 468.75 Ê 006, 5. Ê 007, 473.75 Result of executing program line 004. 30 Program line 005: Result of executing program line 005. 5 Program line 006: 5 Result of executing program line 006. 40 Program line 007: + Result of executing program line 007 (the last line of the program).
Section 8: Programming Basics required amounts for the first item on the invoice manually. The keystroke sequence will use storage register arithmetic (described on page 25) in registers R1, R2, and R3 to calculate the column sums. Since these registers are cleared when fCLEAR² is pressed, we’ll press those keys before beginning the manual calculation – and also later, before running the program – to ensure that the column sums are “initialized” to zero.
Section 8: Programming Basics Keystrokes (RPN mode) Display 6.75?0 fCLEAR² 6.75 0.00 13 \ 13. 13.00 68.5 § ?+1 68.5 890.50 890.50 :0 b ?+2 6.75 60.11 60.11 + ?+3 950.61 950.61 97 Stores tax rate in R0. Clears the registers in R1 through R6. Keys in quantity of item. Separates quantity of item from cost of item to be keyed in next. Keys in cost of item. AMOUNT. Adds AMOUNT to sum of AMOUNT entries in register R1. Recalls tax rate to display. TAX. Adds TAX to sum of TAX entries in register R2.
Section 8: Programming Basics Now, to run the program: Keystrokes (RPN mode) Display fs fCLEAR² 6.75?0 13\68.5 950.61 0.00 t 890.50 60.11 950.61 72.9 18\72.9 t 24\85 t 5\345 t :1 :2 :3 68.5 1,312.20 88.57 1,400.77 85. 2,040.00 137.70 2,177.70 345. 1,725.00 116.44 1,841.44 5,967.70 402.82 6,370.52 Sets calculator to Run mode. Clears registers R1– R6. Stores tax rate. Enters quantity and price of first item on invoice. AMOUNT for first item. TAX for first item. TOTAL for first item.
Section 8: Programming Basics 99 Example: Replace the program above by one containing t instructions instead of u instructions. Keystrokes (RPN mode) Display fs f] fCLEARÎ § t 000, 000, 000, 001, 002, ?+1 :0 b t 003,44 40 004, 45 005, 006, ?+2 + ?+3 fs fCLEAR² 13\68.5 t t t 18\72.9 t t t 24\85 t t t 5\345 t t t :1 007,44 40 008, 009,44 40 6,370.52 0.00 68.5 890.50 60.11 950.61 72.9 1,312.20 88.57 1,400.77 85. 2,040.00 137.70 2,177.70 345. 1,725.00 116.44 1,841.44 5,967.
Section 8: Programming Basics Keystrokes (RPN mode) Display :2 :3 402.82 6,370.52 Sum of TAX column. Sum of TOTAL column. Program execution is also automatically halted when the calculator overflows (refer to page page 73) or attempts an improper operation that results in an Error display. Either of these conditions signifies that the program itself probably contains an error.
Section 9 Branching and Looping Although the instructions in a program normally are executed in order of their program line numbers, in some situations it is desirable to have program execution transfer or “branch” to a program line that is not the next line in program memory. Branching also makes it possible to automatically execute portions of a program more than once – a process called “looping.” Simple Branching The i (go to) instruction is used in a program to transfer execution to any program line.
Section 9: Branching and Looping If you want to terminate the execution of a loop, you can include an o or m instruction (described below) or an t instruction within the loop. You can also terminate execution by pressing any key while the loop is being executed. Example: The following program automatically amortizes the payments on a home mortgage without requiring you to press f! for each payment.
Section 9: Branching and Looping 103 Keystrokes Display gi002 007,43,33,002 Transfers program execution to line 002, so that the number of payments to be amortized can be recalled to the display before the ! instruction in line 003 is executed. Sets calculator to Run mode. 0.00 (Display shown assumes no results remain from previous calculations.) Clears financial registers. 0.00 Enters n. 360.00 Enters i. 1.06 Enters PV. 50,000.00 Sets payment to End. 50,000.00 Calculates the monthly payment. –543.
Section 9: Branching and Looping Keystrokes Display Ê 002, Ê 1.00 003, 42 –531.12 Ê 004, 43 –531.12 005, –12.23 Ê Ê Ê t t(or any key) a 45 0 Line 002: :0. Program execution has branched to the beginning of the loop for the second pass through it. 11 Line 003: f!. Portion of second month’s payment applied to interest. 31 Line 004: gu. 34 Line 005: ~. Portion of second month’s payment applied to principal. 31 Line 006: gu. 006, 43 –12.23 007,43,33,002 Line 007: gi002.
Section 9: Branching and Looping 105 The HP 12C Platinum provides two conditional test instructions that are used in programs for conditional branching: z o tests whether the number in the X-register (represented by the x in the key symbol) is less than or equal to the number in the Y-register (represented by the y in the key symbol).
Section 9: Branching and Looping Example: The following program calculates income tax at a rate of 20% on incomes of $20,000 or less and 25% on incomes of more than $20,000.
Section 9: Branching and Looping 107 Y-registers (as also explained in Appendix A): that is, it will place the income back into the X-register and place the test value into the Y-register.
Section 9: Branching and Looping Keystrokes (RPN mode) 20000?0 20?1 25?2 15000 Display 20,000.00 20.00 25.00 15,000. Stores test value in register R0. Stores 20% tax rate in register R1. Stores 25% tax rate in register R2. Keys income less than test value into display and X-register. 0 Line 001: :0. Test value has been recalled to X-register, moving income to Y-register. 34 Line 002: ~ Income has been placed in X-register and test value has been placed in Y-register.
Section 9: Branching and Looping Keystrokes (RPN mode) Ê Ê Ê Ê 25000 Ê Ê Ê Ê Ê Ê 109 Display 003, 43 34 Line 003 go. 20,000.00 004,43,33,007 Condition tested by o was true, so program execution continued with line 004: gi007. 20,000.00 007, 45 1 Line 007: :1. 20% tax rate has been recalled to 20.00 X-register, moving income to Yregister. 008, 25 Line 008: b. 20% of 20,000 = 4,000. 4,000.00 Keys income greater than test 25,000. value into display and X-register 001, 45 0 Line 001: :0.
Section 10 Program Editing There are various reasons why you might want to modify a program you have stored in Program memory: to correct a program that turns out to have errors; to insert new instructions such as ? to store intermediate results or u to display intermediate results; or to replace a u instruction by an t instruction. Rather than clearing program memory and keying in the modified program, you can modify the program already stored in the calculator. This is called program editing.
Section 10: Program Editing 111 Keystrokes Display Ê 006,43,33,008 Shows that instruction in program line 006 has not been changed. Sets calculator back to Run mode. 6,250.00 (Display shown assumes results remain from last example in preceding section.) Copies tax rate from R2 into R6. 25.00 fs :2?6 Adding Instructions at the End of a Program To add one or more instructions at the end of the last program stored in program memory: 1. Press fs to set the calculator to Program mode. 2. Press gi.
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.
Section 10: Program Editing 113 Example: Assuming you have added a - instruction at the end of program memory as in the preceding example, suppose you now wanted to insert an t instruction before the - instruction so that the program will display the amount of the tax before displaying the net income after tax.
Section 10: Program Editing 4. Press gi. followed by three digits that specify the last line you keyed into program memory. 5. Press gi000. This automatically converts a data storage register into seven additional lines of program memory (if there was not already a i000 instruction remaining at the end of program memory), and it ensures that program execution will branch to line 000 after the program is run. 6. Key in the instruction(s) being added. 7.
Section 10: Program Editing Keystrokes (RPN mode) Display gi.010 010, gi000 :3 ~ go gi000 :0 gi002 fs 7500?3 6500t 15000t t 115 30 Sets calculator to last line of program so that i000 instruction keyed in next will be stored in first line following program. 011,43,33,000 Ensures that i000 instruction follows program. 012, 45 3 013, 34 Added instructions. 014, 43 34 015,43,33,000 016, 45 0 Keys in instruction immediately following point at which new instructions are being added.
Section 10: Program Editing 000, 0 0 1, 43,33,0 1 2 002, 34 0 0 3, 43 34 004, 43,33,007 005, 45 6 006, 43,33, 008 0 0 7, 45 1 008, 25 009, 31 0 1 0, 30 0 1 1, 43,33,000 012, 45 3 0 13, 34 014, 43 34 015, 43,33, 000 016, 45 0 017, 43,33, 0 0 2
Section 11 Multiple Programs You can store multiple programs in program memory, provided that you separate them by instructions that will halt program execution after each program is run and return to the beginning of the program if it is run again. You can run programs after the first one stored in program memory by setting the calculator to the first line of the program using i before pressing t. Storing Another Program To store a program after another program is already stored in program memory: 1.
Section 11: Multiple Programs Example 1: Assuming that program memory still contains the last program from the preceding section (which consisted of 17 program lines), store after that program the office-supplies program from Section 8 (page 86). Since this is the second program to be stored in program memory, we’ll ensure that a i000 instruction separates it from the first program by doing step 3 in the procedure above.
Section 11: Multiple Programs 119 Keystrokes Display fs f] gi.027 Sets calculator to Program mode. 000, Sets RPN mode. 000, 027,43,33,019 Sets calculator to last line keyed into program memory. 028, 44 0 029, 45 0 030, 42 11 Keys in program 031, 43 31 032, 34 033, 43 31 034,43,33,029 ?0 :0 f! gu ~ gu gi029 Running Another Program To run a program that does not begin with program line 001: 1. Press fs to set the calculator to Run mode. If the calculator is already in Run mode, skip this step. 2.
Part III Solutions
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.
Section 12: Real Estate and Lending 123 Example 1: A borrower is charged 2 points for the issuance of his mortgage. If the mortgage amount is $60,000 for 30 years and the interest rate is 11½% per year, with monthly payments, what true annual percentage rate is the borrower paying? (One point is equal to 1% of the mortgage amount.) Keystrokes (RPN mode) Display g fCLEARG 30gA 11.5gC 360.00 0.96 60000$ P :$2b-$ 60,000.00 –594.17 58,800.00 ¼ 0.98 12§ 11.
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 $150? Keystrokes (RPN mode) Display g fCLEARG 30gA 11.5gC 60000$ P :$2b150-$ ¼ 12§ 360.00 0.96 Months (into n) Percent monthly interest rate (into i). Loan amount (into PV). Monthly payment (calculated). 60,000.00 –594.17 58,800.00 58,650.00 Effective mortgage amount (into PV). Monthly interest rate (calculated). 0.98 Annual percentage rate.
Section 12: Real Estate and Lending 125 Example 1: A lender wishes to induce the borrower to prepay a low interest rate loan. The interest rate is 5% with 72 payments remaining of $137.17 and a balloon payment at the end of the sixth year of $2000. If the lender is willing to discount the future payments at 9%, how much would the borrower need to prepay the note? Keystrokes (RPN mode) Display g fCLEARG 72n 9gC 137.17Pa 2000M$ a 72.00 Months (into n). Discount rate (into i). 0.
Section 12: Real Estate and Lending payment, as well as the number of payment periods per year, the price paid for the mortgage, and the balloon payment amount (if it exists). Information is entered as follows: 1. Press g and fCLEARG. 2. Key in the total number of periods until the balloon payment occurs and press n. (If there is no balloon payment, key in the total number of periods and press n.) 3. Key in the periodic payment amount then press P.3 4.
Section 12: Real Estate and Lending 127 Example 2: Using the same information given in example 1, calculate the annual yield if the loan is to be paid in full at the end of the fifth year (from original issuance). (In this case both the payment amount and the balloon must be calculated since they are not given.) Keystrokes (RPN mode) Display g fCLEARG 21gA 9gC 100000Þ$ P Input the number of periods (into n). 252.00 Monthly interest rate (into PV). 0.75 –100,000.00 Mortgage amount (into PV).
Section 12: Real Estate and Lending KEYSTROKES (RPN mode) KEYSTROKES (RPN mode) DISPLAY DISPLAY fs Þ 032, 16 f] M 033, 15 t 034, 31 33 fCLEAR Î 000, M 001, 15 d 035, Ma 002, 15 :n 036, :7 003, z 037, b 004, 25 :4 038, - 005, 30 - 039, :n 006, 45 11 :.
Section 12: Real Estate and Lending KEYSTROKES (RPN mode) KEYSTROKES (RPN mode) DISPLAY 129 DISPLAY 1 023, 1 Þ 057, 16 2 024, 2 $ 058, 13 § 025, 20 ¼ 059, 12 f! 026, 11 :gC 060, 45,43 12 d 027, 33 t 061, 31 d 028, 33 :9 062, 45 9 d 029, 33 gC 063, 43 12 :$ 030, 13 M 064, + 031, 40 fs a 42 45 15 FV is repeated in the program twice to ensure that it is computed and not stored. REGISTERS n: Period i: Apprec.
Section 12: Real Estate and Lending 9. Key in the monthly rent for the alternative housing then press ?8. 10. Key in the savings or alternative investment annual interest rate as a percentage then press ?9. 11. Key in the combined State and Federal marginal tax rate5 as a percentage then press ?.0. 12. Press fCLEARG then key in the number of years involved in the investment; press n. 13. Key in the estimated rate of yearly appreciation as a percentage then press ¼. 14.
Section 12: Real Estate and Lending 131 An alternative would be to rent a similar dwelling at $400 per month and to invest the difference between the purchase cost and rent at 6¼% interest. Your personal income tax rate (marginal) is 25% Federal and 5% State. Which alternative is more financially attractive? Keystrokes (RPN mode) Display fCLEARH 7000?1 30?2 12?3 110?4 65?5 1200?6 8?7 400?8 6.25?9 30?.0 fCLEARG 4n 10¼ 70000$ t t t 0.00 7,000.00 30.00 12.00 110.00 65.00 1,200.00 8.00 400.00 6.25 30.00 30.
Section 12: Real Estate and Lending Keystrokes (RPN mode) Display fCLEARH 0gJ 0gK 8ga 7000gK 4ga 6¼ fl 0.00 0.00 0.00 8.00 7,000.00 4.00 6.00 15,218.35 Initialize. First cash flow. Second through ninth cash flows. Tenth through thirteenth cash flows. Interest. NPV. Leases often call for periodic contractual adjustments of rental payments.
Section 12: Real Estate and Lending Keystrokes Display fCLEARH 500gJ gK 5ga 600gK 12ga 750gK 6ga 13.5gC fl 0.00 500.00 500.00 5.00 600.00 12.00 750.00 6.00 1.13 12,831.75 Initialize. First cash flow. Second thru sixth cash flows. Next twelve cash flows. Last six cash flows. Monthly interest rate Amount to invest to achieve a 13.5% yield.
Section 13 Investment Analysis Partial-Year Depreciation For both income tax purposes and financial analyses, it is valuable to calculate depreciation based on a calendar or fiscal accounting year. When the acquisition date of an asset does not coincide with the start of the year – which is the rule rather than the exception – the amounts of depreciation in the first and last years are computed as fractions of a full year’s depreciation.
Section 13: Investment Analysis ?3 :$ ~ $ :n :1 014 015, 016, 017, 018, 019, 020, 44 45 45 45 3 13 34 30 13 11 1 :$ :M :3 gi030 135 037, 45 13 038, 45 15 039, 30 040, 45 3 041, 43,33,030 fs REGISTERS n: Life i: Unused PV: Dep. Value PMT: Unused FV: Salvage R0: Used R1: #Mos./12 R2: Counter R3: 1st Yr. Dep. R4–R.4: Unused 1. Key in the program. 2. Press fCLEARG. 3. Key in the book value then press $. 4. Key in the salvage value then press M. 5.
Section 13: Investment Analysis 1st year 3rd year 2nd year 4th year 3 year life Example 1: A property has just been purchased for $150,000. The purchase price is allocated between $25,000 for land and $125,000 for improvements (building). The remaining useful life of the building is agreed to be 25 years. There is no salvage value forecasted at the end of the useful life of the building. Thus, the depreciable value and book value is $125,000.
Section 13: Investment Analysis 137 Example 2: A new car was purchased for $6,730 with 4½ months remaining in the year. If the expected life of the car is 5 years, what is the amount of depreciation in the first year? Keystrokes (RPN mode) Display gi000 fCLEARG 6730$ 5n 1\ 4.5t Book value. Life. 6,730.00 5.00 1.00 1.00 504.75 First year: depreciation.
Section 13: Investment Analysis ?3 :$ ~ $ 014, 015, 016, 017, 018, 44 45 3 13 34 30 13 :3 gi026 035, 30 036, 45 3 037,43,33,026 fs REGISTERS n: Life FV: Salvage i: Factor R0: Used R3: 1st Yr. Dep. R4–R.4: Unused PV: Dep. Value R1: #Mos./12 PMT: Unused R2: Counter 1. Key in the program. 2. Press fCLEARG. 3. Key in the book value then press $. 4. Key in the salvage value then press M. 5. Key in the declining-balance factor as a percentage then press ¼. 6.
Section 13: Investment Analysis 139 Keystrokes (RPN mode) Display fCLEARG 50000$ 8000M 150¼ 6n 2\ 4t Book value. Salvage value. Declining-balance factor. Life. Year desired. Second year: depreciation. 50,000.00 8,000.00 150.00 6.00 2.00 2.00 11,458.33 Sum-of-the-Years-Digits Depreciation The following HP 12C Platinum program (written in RPN mode) calculates the sum-of-the-years-digits depreciation for the year desired with the acquisition date occurring at any time during the year.
Section 13: Investment Analysis ?3 :$ ~ $ :n :1 014, 015, 016, 017, 018, 019, 020, 44 3 13 34 30 13 45 11 45 1 45 :$ :M :3 gi030 037, 45 13 038, 45 15 039, 30 040, 45 3 041, 43,33,030 fs REGISTERS n: Life FV: Salvage i: Unused R0: Used R3: 1st Yr. Dep. R4–R.4: Unused PV: Dep. Value R1: #Mos./12 PMT: Unused R2: Counter 1. Key in the program. 2. Press fCLEARG. 3. Key in the book value then press $. 4. Key in the salvage value then press M. 5.
Section 13: Investment Analysis 141 Keystrokes (RPN mode) Display fCLEARG 12000$ 500M 25n 4\ 11t 12,000.00 500.00 25.00 4.00 4.00 781.41 8,238.71 5.00 746.02 7,492.69 ~ t ~ Book value. Salvage value. Life. Year desired. Fourth year: depreciation, remaining depreciable value. Fifth year: depreciation, remaining depreciable value.
Section 13: Investment Analysis ?6 :n ~ ?4 d ?0 1 ?-0 ?2 ?3 f# :6 § ?1 :$ ~ $ \ gF ~ :M ~ :0 1 go gi039 d d 1 gu d 004, 44 6 005, 45 11 006, 34 007, 30 008, 44 4 009, 33 010, 44 0 011, 1 012,44 30 0 013, 44 2 014, 44 3 015, 42 25 016, 45 6 017, 20 018, 44 1 019, 45 13 020, 34 021, 30 022, 13 023, 36 024, 43 40 025, 34 026, 45 15 027, 30 028, 34 029, 45 0 030, 1 031, 43 34 032,43,33,039 033, 33 034, 33 035, 1 036, 43 31 037, 33 0 :0 go gi086 :$ :5 $ 1 ?-4 gi040 :4 n 0 ?6 1 ?-2 ?=0 :5 ?-1 :3 fV ?+1 1
Section 13: Investment Analysis t 1 ?+2 ?-0 f# ?+1 ?5 :$ :M - 038, 039, 040, 44 041, 44 042, 043, 44 044, 045, 046, 047, 40 30 42 40 44 45 45 31 1 2 0 25 1 5 13 15 30 :2 gu d t :6 gm gi074 gi058 143 088, 45 2 089, 43 31 090, 33 091, 31 092, 45 6 093, 43 35 094, 43,33,074 095, 43,33,058 fs REGISTERS n: Life FV: Salvage i: Factor R0: Used PV: Dep. Value R1: Dep. PMT: Unused R2: Counter R3: Used R4: Used R5: Used R6: Used 1. Key in the program. 2. Press fCLEARH. 3.
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 $500. Using a 200% declining-balance factor, generate a depreciation schedule for the instrument’s complete life.
Section 13: Investment Analysis 145 Excess Depreciation When accelerated depreciation is used, the difference between total depreciation charged over a given period of time and the total amount that would have been charged under straight-line depreciation is called excess depreciation. To obtain excess depreciation: 1. Calculate the total depreciation then press \. 2. Key in the depreciable amount (cost less salvage) then press \. Key in the useful life of the asset in years then press z.
Section 13: Investment Analysis This Modified Internal Rate of Return procedure (MIRR) is one of several IRR alternatives which avoids the drawbacks of the traditional IRR technique. The procedure eliminates the sign change problem and the reinvestment (or discounting) assumption by utilizing user stipulated reinvestment and borrowing rates. Negative cash flows are discounted at a safe rate that reflects the return on an investment in a liquid account.
Section 13: Investment Analysis Keystrokes (RPN mode) Display 200000gK 10gCfl Þ$ 20nM 180000ÞgJ 0gK5ga 100000ÞgK 5ga 6gCfl 20n¼ 12§ 200,000.00 657,152.37 Last cash flow. NPV of positive cash flows. 775,797.83 NFV of positive cash flows. -660,454.55 NPV of negative cash flows. Monthly MIRR 0.81 Annual MIRR. 9.
Section 14 Leasing Advance Payments Situations may exist where payments are made in advance (leasing is a good example). These agreements call for extra payments to be made when the transaction is closed. This first procedure finds the periodic payment amount necessary to achieve a desired yield when a number of payments are made in advance. And, given the periodic payment, the second procedure calculates the periodic yield.
Section 14: Leasing 149 If solving for the payment amount will be done repetitively, key in the following HP 12C Platinum program. KEYSTROKES (RPN mode) KEYSTROKES (RPN mode) DISPLAY fs 1 f] Þ fCLEAR Î 000, g 001, 002, 43 42 8 34 $ 003, 004, 005, 006, 007, 008, 45 45 0 1 30 11 2 12 + fCLEAR G :0 :1 n :2 ¼ P 45 :1 :3 ~ z DISPLAY 009, 010, 011, 012, 013, 014, 015, 016, 017, 1 16 14 45 45 13 1 40 3 34 10 fs REGISTERS n: n–#Adv. Pmt. FV: 0 i: i R0: n R3: Loan R4–R.
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 (RPN mode) Display 12?0 3?1 10\12z ?2 750?3t 15\12z ?2t 12.00 3.00 Duration of lease. Number of advance payments. 0.83 64.45 Periodic interest rate. Monthly payment to be received. 65.43 Monthly payment to achieve a 15% yield.
Section 14: Leasing 151 5. Key in the total amount of the loan then press Þ:0:P§+$. 6. Press ¼ to obtain the periodic yield. Example 1: A lease has been written to run for 60 months. The leased equipment has a value of $25,000 with a $600 monthly payment. The lessee has agreed to make 3 payments at the time of closing ($1800). What is the annual yield to the lessor? Keystrokes (RPN mode) Display g fCLEARG 60\3 ?0-n 600P 25000Þ:0 :P§+$ ¼ 12§ 57.00 Number of periodic payments. 3.00 -23,200.00 1.44 17.
Section 14: Leasing REGISTERS n: n–#Adv. Pmts. FV: 0 R3: Loan i: i PV: Used PMT: Pmt. R0: n R4–R.7: Unused R1: Adv. Pmts. R2: Pmt. 1. Key in the program. 2. Key in the total number of payments in the lease then press ?0. 3. Key in the total number of payments made in advance then press ?1. 4. Key in the periodic payment to be received then press ?2. 5. Key in the total amount of the loan, then press ?3; then press t to obtain the periodic yield. 6. For a new case, return to step 2.
Section 14: Leasing KEYSTROKES (RPN mode) KEYSTROKES (RPN mode) DISPLAY fs M f] :n fCLEAR Î 000, g 001, 002, 43 42 8 34 - 003, 004, 005, 006, 007, 008, 009, 010, 011, 012, 013, 45 0 11 1 12 3 15 13 2 40 5 0 1 fCLEAR G :0 n :1 ¼ :3 M $ :2 + ?5 0 :4 45 45 45 44 n Þ P $ :4 + :5 ~ z 153 DISPLAY 014, 015, 016, 45 45 15 11 4 017, 018, 30 11 019, 020, 021, 022, 023, 024, 025, 026, 027, 1 16 14 13 4 40 5 34 10 45 45 fs REGISTERS n: Used.
Section 14: Leasing Example 1: A copier worth $22,000 is to be leased for 48 months. The lessee has agreed to make 4 payments in advance, with a purchase option at the end of 48 months enabling him to buy the copier for 30% of the purchase price. What monthly payment is necessary to yield the lessor 15% annually: Keystrokes (RPN mode) Display 48?0 15\ 12z?1 22000?2 30b?3 4?4t 1.25 Monthly interest rate. 487.29 Monthly payment received by lessor.
Section 14: Leasing 155 4. Key in 0gK then the number of advance payments minus one. Then press ga. 5. Key in the residual then press gK. Then press fL to solve for periodic yield. Example: Equipment worth $5000 is leased for 36 months at $145 per month. The lessee has agreed to pay the first and last month’s payments in advance. At the end of the lease, the equipment may be purchased for $1500.
Section 15 Savings Nominal Rate Converted to Effective Rate Given a nominal interest rate and the number of compounding periods per year, this keystroke procedure computes the effective annual interest rate. 1. Press g and fCLEARG. 2. Key in the annual nominal rate as a percentage, then press \. 3. Key in the number of compounding periods per year, then press nz¼. 4. Key in 100 then press Þ\$. 5. Press M+ to obtain the effective annual interest rate.
Section 15: Savings ¼ 1 005, 006, 12 1 157 fs REGISTERS n: # Periods. FV: Eff. Rate i: Nom. Rate/n R0–R.9: Unused PV: 0 PMT: Used. 1. Key in the program. 2. Key in the annual nominal rate as a percentage then press \. 3. Key in the number of compounding periods per year then press t to obtain the effective annual interest rate. 4. For a new case return to step 2.
Section 15: Savings Nominal Rate Converted to Continuous Effective Rate This procedure converts a nominal annual interest rate to the continuous effective rate. 1. Press 1\. 2. Key in the nominal rate as a percentage then press b. 3. Press g>à. Example: What is the effective rate resulting from a 5¼% passbook rate with continuous compounding? Keystrokes (RPN mode) Display 1\5.25b g> à 1.05 5.39 Continuous rate.
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.
Section 16: Bonds z n gT 1 ~ 018, 019, 020, 021, 022, n: ∆ days/180 FV: Red + Cpn./2 i: Yield/2 R0: Yield R3: Dset R4: Dmat 43 10 11 24 1 34 $ ¼ 2 § 043, 044, 045, 046, 13 12 2 20 fs REGISTERS PV: Price R1: Price. R5: Redemption PMT: Coupon/2. R2: Coupon R6: Coupon/2. R7–R.3: Unused 1. Key in the program. 2. If the C status indicator is not displayed, press ?Æ. 3. Key in the annual coupon interest rate as a percentage then press ?2. 4. Key in the settlement date (MM.
Section 16: Bonds 161 Example 1: What price should you pay on August 28, 2003 for a 5½% bond (computed with a 30/360 basis) that matures on June 1, 2007, if you want a yield of 7¾%? What price should you pay for a yield of 8%? This problem assumes a redemption value of 100. Keystrokes (RPN mode) Display ?Æ 5.5?2 8.282003?3 6.012007?4 100?5 7.75?0 t ~ 8?0 t ~ + 5.50 8.28 6.01 100.00 7.75 92.77 1.33 8.00 92.01 1.33 93.34 Set compound interest mode if the C indicator is not on. Coupon into register 2.
Section 16: Bonds KEYSTROKES (RPN mode) KEYSTROKES (RPN mode) DISPLAY fs :5 f] gÒ DISPLAY ?7 018, 019, 020, 45 43 44 5 26 7 fCLEAR Î 000, fCLEAR G 001, 42 34 :6 021, 45 6 g 002, 003, 004, 005, 006, 007, 008, 009, 010, 011, 012, 013, 014, 015, 016, 017, 43 45 8 0 11 2 14 1 12 3 15 13 5 26 6 16 30 6 :4 022, 023, 024, 025, 026, 027, 028, 029, 030, 031, 032, 033, 034, 035, 036, 45 43 45 4 26 7 10 11 0 14 15 16 11 2 16 20 31 30 :0 n :2 P :1 ¼ :3 M $ :5 Æ 6 Þ ?6 45 45 45 45
Section 16: Bonds 163 For annual coupon bonds calculated on a 30/360 day basis, insert d after gÒ at steps 19 and 23 (making the program two steps longer). 1. Key in the program and press ?Æ if the C status indicator is not displayed. 2. Key in the total number of coupons which are received and press ?0. 3. Key in the annual yield as a percentage then press ?1. 4. Key in the amount of the annual coupon then press ?2.15 5. Key in the redemption value then press ?3.15 6.
Appendixes
Appendix A RPN and the Stack In RPN mode, four special registers in the HP 12C Platinum 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” Displayed or collectively as “the stack.”) The stack registers are designated X, Y, Z, and T.
Appendix A: RPN and the Stack 167 Now let’s see what happens in the stack during a chain calculation in RPN mode: (--------------------------------------3 × 4 ) + ( 5 × 6 )7 Keys See how the intermediate results are not only displayed when they are calculated, but also automatically stored and available in the stack at just the right time! That’s basically how the stack operates.
Appendix A: RPN and the Stack Termination of Digit Entry The first digit keyed in after digit entry has been terminated replaces the number already in the displayed X-register. Digit entry is automatically terminated when any key is pressed (except for digit entry keys – digit keys,., Þ, and É – and prefix keys – f, g,?, :, and i). Stack Lift When the stack lifts, the number in each stack register is copied into the register above, and the number formerly in the T-register is lost.
Appendix A: RPN and the Stack 169 Pressing d four times successively displays the numbers in the Y-, Z-, and T-registers and returns the numbers to their original registers. Keys One-Number Functions and the Stack One-number mathematics and number-alteration functions – y, r, ¿ >, e, B, Ñ, and T – use only the number in the displayed X-register. When the key is pressed, the function is performed upon the number in the X-register, and the answer is then placed into the X-register.
Appendix A: RPN and the Stack calculations shown below, you would put the 8 in the Y-register (using \ and then key the 2 into the displayed X-register. Addition Subtraction Multiplication Division 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.
Appendix A: RPN and the Stack 171 Key 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.
Appendix A: RPN and the Stack The LAST X Register and the F KEY The number in the displayed X-register is copied into the LAST X register whenever any of the following function keys is pressed: + q T R D > Ñ e Ò § ¿ _ b z r ^ à y B Q Z Pressing gF lifts the stack (unless \, O, _, ^, A, or C was the last key pressed, as described on page 168), then copies the number from the LAST X register into the displayed X-register. The number remains also in the LAST X register.
Appendix A: RPN and the Stack 173 The diagram on page 167 illustrates how the automatic stack lift and stack drop make chain calculations quick and error-free. Virtually every chain calculation you are likely to encounter can be done using only the four stack registers.
Appendix A: RPN and the Stack Keystrokes (RPN mode) 2\\ \ 84000 § § § Display Enters constant into Y-, Z-, and T-registers. Enters base amount into displayed 84,000. 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. 2.00 In the example above, the constant was repeatedly multiplied by the result of the previous operation, which was already in the displayed X-register.
Appendix B Algebraic Mode (ALG) To select algebraic mode, press f[. When the calculator is in algebraic mode, the ALG status indicator is lit. Simple Arithmetic calculations in ALG mode To calculate 21.1 + 23.8: Keystrokes (ALG mode) 21.1+ 23.8 } Display 21.10 23.80 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 77.3590.
Appendix B: Algebraic Mode (ALG) Chain Calculations in ALG mode To do a chain calculation, you don’t need to press } after each operation, but only at the very end. 750 × 12 For instance, to calculate --------------------- you can enter either: 360 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. 456 – 75 68 Here’s a longer chain calculation: --------------------- × ------18.5 1.
Appendix B: Algebraic Mode (ALG) 177 Percent Difference To find the percent difference between two numbers: 1. Key in the base number. 2. Press } to separate the other number from the base number. 3. Key in the other number. 4. Press à. Example: Yesterday your stock fell from 35.5 to 31.25 per share. What is the percent change? Keystrokes (ALG mode) Display 35.5} 35.50 31.25 à 31.25 11.97 Keys in the base number and separates it from the other number. Keys in the other number.
Appendix B: Algebraic Mode (ALG) The Power Function Pressing q calculates a power of a number, that is, yx. Like the arithmetic function +, q requires two numbers: 1. Key in the base number (which is designated by the y on the key). 2. Press q and key in the exponent (which is designated by the x on the key) 3. Press } to calculate the power. To Calculate Keystrokes (ALG mode) Display 21.4 2q1.4} 2.64 2–1.4 2q1.4Þ} 0.38 (–2)3 2Þq3} –8.00 3 2q3y} 1.
Appendix C More About L Given a sequence of positive and negative cash flows, we hope that there is enough information to determine whether an IRR answer exists, and what that answer is. For the vast majority of cases, your HP 12C Platinum will find the unique IRR answer if it exists. But the IRR computation is so complex that if the cash flow sequence does not meet certain criteria, then sometimes the calculator is unable to determine whether or not an answer or answers exist.
Appendix C: More About L Your guess will aid the calculator in its search, and if it finds an IRR answer near your guess, that answer will be displayed. Since the calculator cannot tell you the number of solutions that exist when there is more than one mathematically correct answer, you can continue to make guesses, pressing :gt after each one, to search for IRR solutions. You can hasten this process by using the l function to help you make a good guess.
Appendix D Error Conditions Some calculator operations cannot be performed under certain conditions (for example, z when x = 0). If you attempt such an operation under these 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. The symbols x and y represent the number in the X- and Y-registers, respectively, when the operation key is pressed.
Appendix D: Error Conditions Error 2: Statistics Operation Condition Ö h v n (number in R1) = 0 Σx = 0 n=0 n=1 nΣx2 – (Σx)2< 0 nΣy2 – (Σy)2< 0 n=0 nΣx2 – (Σx)2 = 0 n=0 nΣy2 – (Σy)2 = 0 R Q R~ Q~ [nΣx2 – (Σx)2][nΣy)2 – Σy)2)] ≤ 0 Error 3: IRR Refer to Appendix C. Error 4: Memory z Attempting to enter more than 400 program lines. z Attempting to i to a program line that does not exist. z Attempting storage register arithmetic in R5 through R9 or R.0 through R.9.
Appendix D: Error Conditions P M ! l V Ý # E S n=0 i=0 i < –100 When calculating YTM or BOND PRICE and PMT is negative. i < –100 x≤0 x is noninteger. i < –100 n≤0 n > 1010 x≤0 x is noninteger PMT < 0 PMT < 0 Error 6: Storage Registers Operation Condition ? : K a Storage register specified does not exist or has been converted to program lines. n specifies a storage register that does not exist or has been converted to program lines.
Appendix D: Error Conditions Error 8: Calendar Operation Condition Ò D D Improper date format or illegal date. Attempting to add days beyond calculator’s date capacity. Improper date format or illegal date. E S a More than 500 years between settlement (purchase) date and maturity (redemption) date. Maturity date earlier than settlement date. Maturity date has no corresponding coupon date (6 months earlier).
Appendix E Formulas Used Percentage ( x ) × Rate ( x ) % = Base ---------------------------------------------100 NewAmount ( x ) – Base ( y ) ∆% = 100 -------------------------------------------------------------------- Base ( y ) Amount ( x ) %T = 100 ----------------------------- Total ( y ) Interest n i PV FV PMT S I INTG (n) FRAC (n) = = = = = = number of compounding periods. periodic interest rate, expressed as a decimal. present value. future value or balance. periodic payment.
Appendix E: Formulas Used With simple interest used for an odd period: – INTG ( n ) 1 – (1 + i) 0 = PV [ 1 + iFRAC ( n ) ] + ( 1 + iS )PMT ---------------------------------------------- + i FV ( 1 + i ) – INTG ( n ) With compound interest used for an odd period: 0 = PV ( 1 + i ) FV ( 1 + i ) FRAC ( n ) – INTG ( n ) 1 – (1 + i) + ( 1 + iS )PMT ---------------------------------------------- + i – INTG ( n ) Amortization n INTj PRNj PVj = = = = j INT1 = = PRN1 PV1 INTj PRNj PVj = = = = = n
Appendix E: Formulas Used Discounted Cash Flow Analysis Net Present Value NPV CFj = net present value of a discounted cash flow. = cash flow at period j. CF CF CF 1 2 n NPV = CF 0 + ----------------- + ----------------- + … + ----------------- (1 + i) 1 (1 + i) 2 (1 + i) n Internal Rate of Return n CFj IRR k 0= ∑ = number of cash flows = cash flow at period j.
Appendix E: Formulas Used 30/360 Day Basis DAYS = f(DT2) – f(DT1) f(DT) = 360 (yyyy) + 30mm + z for f(DT1) if dd1 = 31 then z = 30 if dd1 ≠ 31 then z = dd1 for f(DT2) if dd2 = 31 and dd1 = 30 or 31 then z = 30 if dd2 = 31 and dd1 < 30 then z = dd2 if dd2 < 31 then z = dd2 Bonds Reference: Spence, Graudenz, and Lynch, Standard Securities Calculation Methods, Securities Industry Association, New York, 1973. DIM = days between issue date and maturity date.
Appendix E: Formulas Used For semiannual coupon with more than 6 months to maturity: RDV PRICE = --------------------------------------------------------DSC 1 + YIELD ------------------ 200 N – 1 + -----------E CPN -----------CPN DCS 2 - – ------------ × -----------+ ∑ --------------------------------------------------------2 E K – 1 + DSC -----------E K=1 1 + YIELD ------------------ 200 N Depreciation L SBV SAL FACT = = = = j DPNj RDVj = = = RBVj = Y1 = asset’s useful life expec
Appendix E: Formulas Used Sum-of-the-Years-Digits Depreciation ( W + 1 ) ( W + 2F ) SOYDk = -----------------------------------------2 where W = integer part of k F = fractional part of k. (i.e., for k = 12.25 years, W = 12 and F = 0.25).
Appendix E: Formulas Used 1 --- NFV n MIRR = 100 --------------P- – 1 NPV N Advance Payments A = number of payments made in advance. –n PV – FV ( 1 + i ) PMT = -------------------------------------------------------–( n – A ) – (1 + i) 1----------------------------------------+A i Interest Rate Conversions C EFF NOM = number of compounding periods per year. = the effective annual interest rate as a decimal. = the nominal annual interest rate as a decimal.
Appendix E: Formulas Used Weighted Mean ∑ wx x w = -------------∑w Linear Estimation n = number of data pairs ŷ = A + Bx – Ax̂ = y----------B ∑ x ⋅ ∑ y∑ xy – ----------------------n where B = -----------------------------------------2 ∑x 2 (∑ x) – ----------------2 A = y – Bx ∑ x ⋅ ∑ y∑ xy – ----------------------n r = ------------------------------------------------------------------------------------------2 (∑ x) – - ⋅ x ∑ ---------------n 2 2 (∑ y) y – ∑ ---------------n 2 Standard Dev
Appendix E: Formulas Used 193 n n! = ∏i i=1 The Rent or Buy Decision Market Value = PRICE(1 + I)n where: I n = appreciation per year (as decimal) = number of years Net Cash Proceeds on Resale = Market Value – Mortgage Balance – Commission The interest rate is obtained by solving the financial (compound interest) equation for i using: n = number of years house is owned PV = down payment + closing costs PMT = mortgage payment + taxes + maintenance – rent – (% tax) (interest + taxes) FV = net cash proc
Appendix F Battery, Warranty, and Service Information Battery The HP 12C Platinum 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. Low-Power Indication A battery symbol ( ) shown in the upper-left corner of the display when the calculator is on signifies that the available battery power is running low.
Appendix F: Battery, Warranty, and Service Information To install a new battery, use the following procedure: 1. With the calculator turned off, slide the battery cover off. 2. Remove the old battery. 3. Insert a new battery, with positive polarity facing outward. 4. Replace the battery cover. Note: Be careful not to press any keys while the battery is out of the calculator.
Appendix F: Battery, Warranty, and Service Information 197 For a calculator that does not respond to keystrokes: 1. Insert a thin, pointed object all the way into the reset hole near the battery compartment and then remove it. 1. The display will show Pr Error. Pressing any key will clear this message from the display. 2. If the calculator still does not respond to keystrokes, remove and re-insert the battery. Make sure that the battery is properly positioned in the battery compartment. 3.
Appendix F: Battery, Warranty, and Service Information Note: Tests of the calculator’s electronics are also performed if the = key or the z key is held down when ; is released.3 These tests are included in the calculator to be used in verifying that it. is operating properly during manufacturing and service. If you had suspected that the calculator was not working properly but the proper display was obtained in step 2, it is likely that you made an error in operating the calculator.
Appendix F: Battery, Warranty, and Service Information 199 entitled to a refund of the purchase price upon prompt return of the product. 4. HP products may contain remanufactured parts equivalent to new in performance or may have been subject to incidental use. 5.
Appendix F: Battery, Warranty, and Service Information Service Argentina Austria Belgium Brazil Canada Central America & Caribbean Chile Columbia Costa Rica Czech Republic Denmark Eastern Europe countries Finland France Germany Greece Guatemala Holland Israel Italy Luxembourg Mexico Norway Peru Poland Portugal Puerto Rico Spain Sweden Switzerland Turkey UK USA Venezuela 0-810-555-5520 +43-1-3602771203 +32-2-7126219 Sao Paulo 3747-7799; elsewhere 0-800-157751 +1 905 206 4663 1-800-711-2884 800-360999
Appendix F: Battery, Warranty, and Service Information 201 Potential For Radio/Television Interference (for U.S.A. Only) The HP 12C Platinum generates and uses radio frequency energy and if not installed and used properly, that is, in strict accordance with the manufacturer’s instructions, may cause interference to radio and television reception.
Appendix F: Battery, Warranty, and Service Information Regulation applying to The Netherlands A battery is delivered with this product. When empty, do not throw it away, but collect it as small chemical waste. Bij dit produkt zijn betterijen geleverd.Wanneer deze leeg zijn, moet u ze niet weggooien maar inleverenals KCA.
Appendix G 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.
Appendix G: United Kingdom Calculations Bond Calculations Solutions for the price and yield to maturity of United Kingdom bonds are not included in this handbook. Actual practice differs according to the type of bond; variations such as cumulative and ex-dividend pricing, simple or compound interest discounting, etc., may be encountered. Application Notes covering such situations may be available in the United Kingdom; check with your local authorized Hewlett-Packard dealer.
Function Key Index General ; Power on /off key (page 16). f Shift key. Selects alternate function in gold above the function keys (page 16). Also used in display formatting (page 71). g Shift key. Selects alternate function in blue on the slanted face of the function keys (page 16). CLEARX after f, g, ?, :or i, cancels that key (page 18). fCLEARX also displays mantissa of number in the displayed X-register (page 73). Digit Entry \ Enters a copy of number in displayed X-register into Y-register.
Function Key Index  Sets payment mode to End for compound interest calculations involving payments (page 39). Ï Calculates simple interest (page 35). w Stores or computes number of periods in financial problem (page 34). A Multiplies a number in displayed X-register by 12 and stores the resulting value in the n-register (page 41). ¼ Stores or computes interest rate per compounding period (page 34).
Function Key Index R Linear estimate (X-register), correlation coefficient (Y-register). Fits a line to a set of (x,y) data pairs entered using _, then extrapolates this line to estimate a y-value for a given x-value. Also computes strength of linear relationship (r) among that set of (x, y) data pairs (page 79). Q Linear estimate (X-register), correlation coefficient (Y-register).
Programming Key Index s Program/Run. Toggles into and out of Program mode. Automatically sets program to line 000 when returning to Run mode (page 86). N Memory map. Describes the current allocation of memory; the number of lines allotted to program memory and the number of available data registers (page 93). Program Mode Run Mode In Program mode, function keys are recorded in program memory. Display shows program memory line number and the keycode (keyboard row and location in row) of the function key.
Programming Key Index Program Mode Active Keys: i Go to. Followed by a decimal point and a three-digit number, positions calculator to that line in program memory. No instructions are executed (page 93) Ê Single step. Displays line number and contents of next program memory line. If held down, displays line number and contents of all program memory lines, one at a time (page 90). Ü Back step. Displays line number and contents of previous program memory line.
Subject Index A Adding instructions 111–115 Advance payments 148, 152 Algebraic mode 19, 175 ! 12, 55, 168 Amortization 40, 54–57, 186 Annual interest rate 41 Annual Percentage Rate 53–54, 122–124, 203 Annuities 38 Annuities, deferred 131–133 Annuity due 39–40 Appreciation 40 APR, See Annual Percentage Rate Arithmetic calculations with constants 75, 173 Arithmetic calculations, chain 20–23 Arithmetic calculations, simple 19 Arithmetic operations and the stack 169 Arithmetic, storage register 25 Asterisk in
Index Branching, adding instructions by 113–115 Branching, conditional 104–106 Branching,simple 101 Ü 90 Buying versus Renting 127 C C status indicator 53 Calendar functions 30–33, 187–188 Calendar functions and the stack 171 J 61 Cash flow diagram 36–40 Cash flow sign convention 35, 38 K 60, 62, 64 Cash flows, changing 66 Cash flows, reviewing 64 Cash flows, storing for I and L 59, 66 Chain calculations 20–23, 172–173, 176 Þ 17, 20, 35, 59 O 18, 29 Clearing display 18 Clearing financial registers 18
Index D D 30–33 D.
Index Exponent 18, 84 Exponential 82 F Factorial 82 Financial registers 34 Financial registers, clearing 34 Fractional 83 Future value 38 Future value, calculating 49 FV 38 G–K i 91 Indicators, status 70 Instructions in program lines 89 ¼ 12 Ï 168 Interest rate, annual 45 Interest rate, periodic 45 Interest, simple 35 Internal rate of return 58 Internal rate of return, calculating 63 Internal rate of return, modified 145 Interrupting a program 95 IRR 58, 145 L 12 Keyboard 16 L LAST X register 70 Le
Index M Mantissa 18, 73 Mantissa Display Format 73 Mean 77 Ö 168 Mean, weighted 81 memory 23 Memory, program 91 Modes alegebraic 19 RPN 19 Modified internal rate of return 145 Mortgage, price of 124 Mortgage, yield of 125 Multiple programs 117 N Negative numbers 17, 175 Net amount 27 Net present value 58 Net present value, calculating 59 Nominal interest rate, converting 156 Nominal rate 158 NPV 58 Number display formats 71 Numbers, keying in 17 Numbers, large 18 Numbers, negative 17 Numbers, recalling 24
Index P Partial-year depreciation 134 Payment 38, 152 Payment amount, calculating 48 Payment mode 38 Payments, advance 148, 152 Payments, number of 41 Percent difference 28, 177 Percent of total 29, 177 Percentages 27, 176 PMT 38 Populations 79 Power function 84, 178 Pr error 74 Prefix key 16 Present value 38 Present value, calculating 46 PRGM status indicator 86, 87 Program branching 101 Program editing 110 Program lines, displaying 90 Program looping 101 Program memory 88, 91 Program mode 86 Program
Index Residual 152 E 168 Round 82 B 82 Rounding 71 RPN mode 19, 20, 166 Running message 12, 63 S v 168 Samples 79 Savings 156 Scientific notation 72 scientific notation 18 Simple branching 101 Simple interest 35 V 168 Ý 168 Square Root 82 Stack 166 Standard deviation 78 Statistics 76 Status indicators 70 ? 24 Storage register arithmetic 25 Storage registers, clearing 25 Storing numbers 34 Storing programs 117 Straightline depreciation 134 Sum-of-the-years -digits depreciation 139 T–Z Two-variable statist
