hp 12c platinum financial calculator user's guide H Edition 4 HP part number F2232-90001 File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 1 of 275 Printed Date: 2005/8/1 Dimension: 14.
Notice REGISTER YOUR PRODUCT AT: www.register.hp.com THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED “AS IS” AND ARE SUBJECT TO CHANGE WITHOUT NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WARRANTY OF ANY KIND WITH REGARD TO THIS MANUAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY, NON-INFRINGEMENT AND FITNESS FOR A PARTICULAR PURPOSE. HEWLETT-PACKARD CO.
Introduction About This Handbook This hp 12c platinum user's guide is intended to help you get the most out of your investment in your hp 12c platinum Programmable Financial Calculator. Although the excitement of acquiring this powerful financial tool may prompt you to set this handbook aside and immediately begin “pressing buttons,” in the long run you’ll profit by reading through this handbook and working through the examples it contains.
Introduction z The various appendices describe additional details of calculator operation as well as warranty and service information. z The Function Key Index and Programming Key Index at the back of the handbook can be used as a handy page reference to the comprehensive information inside the manual.
Contents Introduction.................................................................... 3 About This Handbook .....................................................................3 Financial Calculations in the United Kingdom.....................................4 For More Solutions to Financial Problems...........................................4 Part I: Problem Solving ......................................... 15 Section 1: Getting Started .................................................
Contents Percent of Total in ALG Mode ................................................. 36 Calendar Functions ...................................................................... 37 Date Format ......................................................................... 37 Future or Past Dates............................................................... 38 Number of Days Between Dates ............................................. 40 Section 3: Basic Financial Functions ................................
Contents 7 Status Indicators ....................................................................87 Number Display Formats ........................................................87 Scientific Notation Display Format ...........................................88 Special Displays ....................................................................90 The Key in RPN Mode..........................................................90 The Key in RPN Mode .........................................................
Contents Looping.................................................................................... 126 Conditional Branching ............................................................... 129 Section 10: Program Editing ............................................... 139 Changing the Instruction in a Program Line ................................... 139 Adding Instructions at the End of a Program.................................. 140 Adding Instructions within a Program ..............................
Contents 9 Section 15: Savings .......................................................... 213 Nominal Rate Converted to Effective Rate ......................................213 Effective Rate Converted to Nominal Rate ......................................215 Continuous Rate Converted to Effective Rate...................................216 Section 16: Bonds ............................................................. 217 30/360 Day Basis Bonds ...........................................................
Contents Error 2: Statistics........................................................................ 246 Error 3: IRR............................................................................... 246 Error 4: Memory ....................................................................... 246 Error 5: Compound Interest ..........................................................247 Error 6: Storage Registers ............................................................248 Error 7: IRR .....................
Contents 11 Low-Power Indication ..................................................................259 Installing a New Battery .......................................................260 Verifying Proper Operation (Self-Tests)...........................................261 Warranty ..................................................................................263 Service .....................................................................................264 Regulatory Information ......................
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 13 Note: A battery symbol ( ) shown in the upper-left corner of the display when the calculator is on signifies that the available battery power is nearly exhausted. To install new batteries, refer to Appendix F. The calendar functions and nearly all of the financial functions take some time to produce an answer. (This is typically just a few seconds, but the¼, !, L, and S functions could require a half-minute or more.
Making Financial Calculations Easy Keystrokes M Display 10,371.79 Value of policy in 14 years. Example 3: The preceding example showed that the insurance policy will provide about half the required amount. An additional amount must be set aside to provide the balance (21,396.61 – 10,371.79 = 11,024.82). Suppose you make monthly payments, beginning at the end of next month, into an account that pays 6% annually, compounded monthly.
Part I Problem Solving File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 15 of 275 Printed Date: 2005/8/1 Dimension: 14.
Section 1 Getting Started Power On and Off To begin using your hp 12c platinum, press the ; key*. Pressing ; again turns the calculator off. If not manually turned off, the calculator will turn off automatically 12 minutes after it was last used. Low-Power Indication A battery symbol ( ) shown in the upper-left corner of the display when the calculator is on signifies that the available battery power is nearly exhausted. To replace the batteries, refer to Appendix F.
Section 1: Getting Started 17 Throughout this handbook, references to the functions shown on the keyboard in gold under the bracket labeled “ CLEAR” appear throughout this handbook preceded by the word “CLEAR” (for example, “The CLEARH function …” or “Pressing fCLEARH …”). If you press the f or g prefix key mistakenly, you can cancel it by pressing fCLEARX. This can also be pressed to cancel the ?, :, and i keys.
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 Keystrokes (ALG mode) 19 Display 12345gÚgÚ .63+ 123.63 Correcting removes the 4 and 5. gÚ clears the most recent digit entered. 5} 128.63 } is also labeled the \ key. gÚ 0.00 Clears the calculator line. The CLEAR Keys Clearing a register or the display replaces the number in it with zero. Clearing program memory replaces the instructions there with gi000.
Section 1: Getting Started Undo Operation Every time you press O, gÚ, fCLEARH, fCLEAR² or fCLEARG key to clear data, the status indicator appears in the display. This means you can press gß to undo the last operation (i.e., to recover the data.) Note: the Undo function is only available immediately after data has been cleared. When the Undo indicator is turned off no operation can be undone.
Section 1: Getting Started 21 Simple Arithmetic Calculations in RPN Mode In RPN mode, any simple arithmetic calculation involves two numbers and an operation — addition, subtraction, multiplication, or division. To do such a calculation on your hp 12c platinum, you first tell the calculator the two numbers, then tell the calculator the operation to be performed. The answer is calculated when the operation key (+,-,§, or z) is pressed.
Section 1: Getting Started Simple Arithmetic Calculations in ALG Mode In ALG mode, any simple arithmetic calculation involves two numbers and an operation — addition, subtraction, multiplication, or division. To do such a calculation on your hp 12c platinum, you tell the calculator the first number, then the operation to be performed, and then tell the calculator the second number. The answer is calculated when the equals key (}) is pressed. For example, to calculate 21.1 + 23.
Section 1: Getting Started 23 Chain Calculations in RPN Mode Whenever the answer has just been calculated and is therefore in the display, you can perform another operation with this number by simply keying in the second number and then pressing the operation key: you need not press \ to separate the second number from the first. This is because when a number is keyed in after a function key (such as +,-,§, z, etc.
Section 1: Getting Started Keystrokes (RPN mode) Display - 21.68 Pressing - subtracts the number just entered from the number previously in the display. The calculator displays the result of this calculation, which is the balance after subtracting the second check. 10.14- 11.54 Keys in the next number and subtracts it from the previous balance. The new balance appears in the display. (It’s getting rather low!) 1053+ 1,064.
Section 1: Getting Started 25 Your hp 12c platinum calculates the answer in just the same way in RPN mode: Keystrokes (RPN mode) Display 3\4§ 12.00 Step 1: Multiply the numbers in the first parentheses. 5\6§ 30.00 Step 2: Multiply the numbers in the second parentheses. + 42.00 Step 3: Add the results of the two multiplications. Notice that before doing step 2, you did not need to store or write down the result of step 1: it was stored inside the calculator automatically.
Section 1: Getting Started Chain Calculations in ALG Mode To do a chain calculation, you don’t need to press } after each operation, but only at the very end. For instance, to calculate 750x12 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. Here’s a longer chain calculation: 456 − 75 68 × 18.5 1.9 This calculation can be written as: 456 – 75 ÷ 18.5 × 68 ÷ 1.9.
Section 1: Getting Started If you want to calculate 27 8 , use the following keystrokes: (5 − 1) Keystrokes (ALG mode) Display OO 0.00 Clears any pending operations. 8zgØ5- 5.00 No calculation is done. 1gÙ 4.00 Calculates 5 − 1. ³ 2.00 Calculates 8 . (5 − 1) Storage Registers Numbers (data) in the hp 12c platinum are stored in memories called “storage registers” or simply “registers.
Section 1: Getting Started Example: Before you leave to call on a customer interested in your personal computer, you store the cost of the computer ($1,250) and also the cost of a printer ($500) in data storage registers. Later, the customer decides to buy six computers and one printer. You recall the cost of the computer, multiply by the quantity ordered, and then recall and add the cost of the printer to get the total invoice. Keystrokes Display 1250?0 1,250.
Section 1: Getting Started 29 Clearing Storage Registers To clear a single storage register — that is, to replace the number in it with zero — merely store zero into it. You need not clear a storage register before storing data into it; the storing operation automatically clears the register before the data is stored. To clear all storage registers at once — including the financial registers, the stack registers, and the LAST X register — press fCLEARH.* This also clears the display.
Section 1: Getting Started Keystrokes Display 22.95?-0 22.95 Subtracts the first check from the balance in R0. Note that the display continues to show the amount subtracted; the answer is placed only in R0. 13.7?-0 13.70 Subtracts the second check. 10.14?-0 10.14 Subtracts the third check. 1053?+0 1,053.00 Adds the deposit. :0 1,064.54 Recalls the number in R0 to check the new balance.
Section 2 Percentage and Calendar Functions Percentage Functions The hp 12c platinum includes three keys for solving percentage problems: b, à, and Z. You don’t need to convert percentages to their decimal equivalents; this is done automatically when you press any of these keys. Thus, 4% need not be changed to 0.04; you key it in the way you see and say it: 4b. Percentages in RPN Mode In RPN mode, to find the amount corresponding to a percentage of a number: 1. Key in the base number. 2. Press \. 3.
Section 2: Percentage and Calendar Functions Percentages in ALG Mode In ALG mode, to find the amount corresponding to a percentage of a number: 1. Key in the base number. 2. Press §. 3. Key in the percentage. 4. Press b. 5. Press }. For example, to find 14% of $300: Keystrokes (ALG mode) Display OO 0.00 Clears any pending operations. 300 300. Keys in the base number. § 300.00 Tells the calculator to multiply the 300 by the percentage entered next. 14 14. Keys in the percentage. b 0.
Section 2: Percentage and Calendar Functions 33 Net Amount in RPN Mode A net amount — that is, the base amount plus or minus the percentage amount — can be calculated easily with your hp 12c platinum, since the calculator holds the base amount inside after you calculate a percentage amount. To calculate a net amount, simply calculate the percentage amount, then press = or -. Example: You’re buying a new car that lists for $23,250. The dealer offers you a discount of 8%, and the sales tax is 6%.
Section 2: Percentage and Calendar Functions Keystrokes (ALG mode) Display 8b 1,860.00 = 21,390.00 Base amount less discount. 6b 1,283.40 } 22,673.40 Total cost: base amount less discount Amount of discount. Amount of tax (on $21,390). plus tax. Percent Difference In RPN or ALG mode, to find the percent difference between two numbers: 1. Key in the base number. 2. Press \ to separate the other number from the base number. 3. Key in the other number. 4. Press à.
Section 2: Percentage and Calendar Functions 35 Percent of Total in RPN Mode In RPN mode, to calculate what percentage one number is of another: 1. Calculate the total amount by adding the individual amounts, just as in a chain arithmetic calculation. 2. Key in the number whose percentage equivalent you wish to find. 3. Press Z. Example: Last month, your company posted sales of $3.92 million in the U.S., $2.36 million in Europe, and $1.67 million in the rest of the world.
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.
Section 2: Percentage and Calendar Functions 37 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.
Section 2: Percentage and Calendar Functions For example, to key in April 7, 2004: Keystrokes Display 4.072004 4.072004 Day-Month-Year. To set the date format to day-month-year, press gÔ. To key in a date with this format in effect: 1. Key in the one or two digits of the day. 2. Press the decimal point key (.). 3. Key in the two digits of the month. 4. Key in the four digits of the year. For example, to key in 7 April, 2004: Keystrokes Display 7.042004 7.
Section 2: Percentage and Calendar Functions 39 Example: If you purchased a 120-day option on a piece of land on 14 May 2004, what would be the expiration date? Assume that you normally express dates in the day-month-year format. Keystrokes Display gÔ 7.04 Sets date format to day-month-year. (Display shown assumes date remains from preceding example. The full date is not now displayed because the display format is set to show only two decimal places, as described in Section 5.) 14.052004\ 14.
Section 2: Percentage and Calendar Functions Number of Days Between Dates To calculate the number of days between two given dates: 1. Key in the earlier date and press \. 2. Key in the later date and press gÒ. The answer shown in the display is the actual number of days between the two dates, including leap days (the extra days occurring in leap years), if any. In addition, the hp 12c platinum also calculates the number of days between the two dates on the basis of a 30-day month.
Section 3 Basic Financial Functions The Financial Registers In addition to the data storage registers discussed on page 27, the hp 12c platinum has five special registers in which numbers are stored for financial calculations. These registers are designated n, i, PV, PMT, and FV.
Section 3: Basic Financial Functions Clearing the Financial Registers Every financial function uses numbers stored in several of the financial registers. Before beginning a new financial calculation, it is good practice to clear all of the financial registers by pressing fCLEARG. Frequently, however, you may want to repeat a calculation after changing a number in only one of the financial registers. To do so, do not press fCLEARG; instead, simply store the new number in the register.
Section 3: Basic Financial Functions 43 Example 1: Your good friend needs a loan to start his latest enterprise and has requested that you lend him $450 for 60 days. You lend him the money at 7% simple interest, to be calculated on a 360-day basis. What is the amount of accrued interest he will owe you in 60 days, and what is the total amount owed? Keystrokes Display (RPN mode) 60n 60.00 Stores the number of days. 7¼ 7.00 Stores the annual interest rate. 450Þ$ –450.00 Stores the principal. fÏ 5.
Section 3: Basic Financial Functions Financial Calculations and the Cash Flow Diagram The concepts and examples presented in this section are representative of a wide range of financial calculations. If your specific problem does not appear to be illustrated in the pages that follow, don’t assume that the calculator is not capable of solving it.
Section 3: Basic Financial Functions 45 The arrow pointing up at the right of the diagram indicates that money is received at the end of the transaction. Every completed cash flow diagram must include at least one cash flow in each direction. Note that cash flows corresponding to the accrual of interest are not represented by arrows in the cash flow diagram.
z Section 3: Basic Financial Functions FV — the future value — is the final cash flow or the compounded value of a series of prior cash flows. In the particular problem illustrated above, FV is unknown (but can be calculated). Solving the problem is now basically a matter of keying in the quantities identified in the cash flow diagram using the corresponding keys, and then calculating the unknown quantity by pressing the corresponding key.
Section 3: Basic Financial Functions 47 The BEGIN status indicator is lit when the payment mode is set to Begin. If BEGIN is not lit, the payment mode is set to End. The payment mode remains set to what you last specified until you change it; it is not reset each time the calculator is turned on. However, if Continuous Memory is reset, the payment mode will be set to End.
Section 3: Basic Financial Functions File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 48 of 275 Printed Date: 2005/8/1 Dimension: 14.
Section 3: Basic Financial Functions 49 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.* 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 51 Keystrokes (RPN mode) Display n 328.00 Number of payments required. 12z 27.33 Twenty-seven years and four months. In ALG mode, perform the RPN steps but replace the last step with the step below. Keystrokes (ALG mode) Display z12} 27.33 Twenty-seven years and four months.
Section 3: Basic Financial Functions Keystrokes (ALG mode) Display +:P –325.00 Recalls payment amount. } –143.11 Final, fractional payment. Alternatively, you could make the fractional payment together with the 327th payment. (Doing so will result in a somewhat smaller total of all payments, since you will not have to pay interest during the 328th payment period.
Section 3: Basic Financial Functions 53 Example 2: You’re opening a savings account today (the middle of the month) with a $775 deposit. The account pays 6.25% interest compounded semimonthly. If you make semimonthly deposits of $50 beginning next month, how long will it take for your account to reach $4,000? Keystrokes (RPN mode) Display fCLEARG 6.25\24z¼ 0.26 Calculates and stores i. 775Þ$ –775.00 Stores PV (with minus sign for cash paid out). 50ÞP –50.
Section 3: Basic Financial Functions Keystrokes (ALG mode) Display g 4,000.00 Sets the payment mode to End. n 58.00 Number of semimonthly deposits. z2} 29.00 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. You can calculate this final, fractional, 58th deposit as in Example 1, except that for this example you must subtract the original FV. (In Example 1, the original FV was zero.
Section 3: Basic Financial Functions Keystrokes (ALG mode) Display 4000} –22.73 55 Calculates final, fractional, 58th deposit required to reach $4,000. Calculating the Periodic and Annual Interest Rates 1. Press fCLEARG to clear the financial registers. 2. Enter the number of payments or periods, using n or gA. 3. Enter at least two of the following values: z Present value, using $. z Payment amount, using P. z Future value, using M. Note: Remember to observe the cash flow sign convention. 4.
Section 3: Basic Financial Functions Keystrokes (RPN mode) Display ¼ 1.61 Periodic (quarterly) interest rate. 4§ 6.44 Annual interest rate. Keystrokes (ALG mode) Display fCLEARG 8§4w 32.00 6000Þ$ –6,000.00 Stores PV (with minus sign for cash Calculates and stores n. paid out). 10000M 10,000.00 Stores FV. ¼ 1.61 Periodic (quarterly) interest rate. §4} 6.44 Annual interest rate. Calculating the Present Value 1. Press fCLEARG to clear the financial registers. 2.
Section 3: Basic Financial Functions 57 Example 1: You’re financing a new car purchase with a loan from an institution that requires 5.9% interest compounded monthly over the 4-year term of the loan. If you can make payments of $450 at the end of each month and your down payment will be $1,500, what is the maximum price you can pay for the car? (Assume the purchase date is one month prior to the date of the first payment.) Keystrokes (RPN mode) Display fCLEARG 4gA 48.00 Calculates and stores n. 5.
Section 3: Basic Financial Functions Example 2: A development company would like to purchase a group of condominiums with an annual net cash flow of $17,500. The expected holding period is 5 years, and the estimated selling price at that time is $540,000. Calculate the maximum amount the company can pay for the condominiums in order to realize at least a 12% annual yield. Keystrokes Display fCLEARG 5n 5.00 Stores n. 12¼ 12.00 Stores i. 17500P 17,500.00 Stores PMT.
Section 3: Basic Financial Functions 59 5. Press g× or g to set the payment mode. 6. Press P to calculate the payment amount. Example 1: Calculate the payment amount on a 29-year, $243,400 mortgage at 5.25% annual interest, compounded monthly. Keystrokes Display fCLEARG 29gA 348.00 Calculates and stores n. 5.25gC 0.44 Calculates and stores i. 243400$ 243,400.00 Stores PV. g 243,400.00 Sets payment mode to End. P –1,363.29 Monthly payment (with minus sign for cash paid out).
Section 3: Basic Financial Functions Keystrokes (RPN mode) Display fCLEARG 15\2µw 30.00 Calculates and stores n. 9.75\2z¼ 4.88 Calculates and stores i. 3200Þ$ –3,200.00 Stores PV (with minus sign for cash paid out). 60000M 60,000.00 Stores FV. g 60,000.00 Sets payment mode to End. P –717.44 Keystrokes (ALG mode) Display Semiannual payment (with minus sign for cash paid out). fCLEARG 15µ2w 30.00 Calculates and stores n. 9.75z2¼ 4.88 Calculates and stores i. 3200Þ$ –3,200.
Section 3: Basic Financial Functions 61 Example 1: In Example 1 on page 59, we calculated that the payment amount on a 29-year, $243,400 mortgage at 5.25% annual interest compounded monthly is $1,363.29. If the seller requests a balloon payment at the end of 5 years, what would be the amount of the balloon? Keystrokes Display fCLEARG 5gA 60.00 Calculates and stores n. 5.25gC 0.44 Calculates and stores i. 243400$ 243,400.00 Stores PV. 1363.29ÞP –1,363.
Section 3: Basic Financial Functions Keystrokes Display fCLEARG 2gA 24.00 Calculates and stores n. 6.25gC 0.52 Calculates and stores i. 50ÞP –50.00 Stores PMT (with minus sign for cash paid out). g× –50.00 Sets payment mode to Begin. M 1,281.34 Balance after 2 years. 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 63 Odd-Period Calculations The cash flow diagrams and examples presented so far have dealt with financial transactions in which interest begins to accrue at the beginning of the first regular payment period. However, interest often begins to accrue prior to the beginning of the first regular payment period.
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.
Section 3: Basic Financial Functions 65 Example 1: A 36-month loan for $4,500 accrues interest at a 5% annual percentage rate (APR), with the payments made at the end of each month. If interest begins accruing on this loan on February 15, 2004 (so that the first period begins on March 1, 2004), calculate the monthly payment, with the odd days counted on the basis of a 30-day month and compound interest used for the odd period. Keystrokes (RPN mode) Display fCLEARG Clears financial registers.
Section 3: Basic Financial Functions Keystrokes (ALG mode) Display 2.152004} 2.15 Keys in the date interest begins accruing and separates it from the next date entered. 3.012004 3.012004 Keys in the date of the beginning of the first period. gÒ 15.00 Actual number of odd days. ~ 16.00 Number of odd days counted on the basis of a 30-day month. z30+ 0.53 Divides by the length of a monthly period to get the fractional part of n. 36n 36.
Section 3: Basic Financial Functions 67 Keystrokes (RPN mode) Display 42+n 42.43 Adds the fractional part of n to the number of complete payment periods, then stores the result in n. 3950$ 3,950.00 Stores PV. 120ÞP –120.00 Stores PMT (with minus sign for cash paid out). ¼ 1.16 Periodic (monthly) interest rate. 12§ 13.95 Annual percentage rate (APR). Keystrokes (ALG mode) Display fCLEARG Clears financial registers.
Section 3: Basic Financial Functions Before leaving this Odd-Period mode example, you may now press ?Æ to turn the C annunciator off, if needed. Note that when the calculator is not in Odd-Period mode, the status of the C annunciator actually has no effect on calculator operation. You will find another use of Odd-Period mode and ?Æ in Section 16 of this manual, where the C must be set before the two Bond programs will work correctly.
Section 3: Basic Financial Functions 69 Amortization The hp 12c platinum enables you to calculate the amounts applied toward principal and toward interest from a single loan payment or from several payments, and also tells you the remaining balance of the loan after the payments are made.* To obtain an amortization schedule: 1. Press fCLEARG to clear the financial registers. 2. Enter the periodic interest rate, using ¼ or gC. 3. Enter the amount of the loan (the principal), using $. 4.
Section 3: Basic Financial Functions Keystrokes Display 1498.12ÞP –1,498.12 Enters PMT (with minus sign for cash paid out). g –1,498.12 Sets payment mode to End. 12f! –13,006.53 Portion of first year’s payments (12 months) applied to interest. ~ –4,970.91 Portion of first year’s payments applied to principal. :$ 245,029.09 Balance remaining after 1 year. :n 12.00 Total number of payments amortized.
Section 3: Basic Financial Functions Keystrokes Display 1f! –1,093.75 Portion of first payment applied to 71 interest. ~ –404.37 1f! –1,091.98 Portion of second payment applied to Portion of first payment applied to principal. interest. ~ –406.14 Portion of second payment applied to principal. :n 2.00 Total number of payments amortized. If you want to generate an amortization schedule but do not already know the monthly payment: 1. Calculate PMT as described on page 58. 2.
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: fl (net present value) and fL (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 z z z 73 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.
Section 4: Additional Financial Functions In summary, to enter the cash flow amounts: 1. Press fCLEARH to clear the financial and storage registers. 2. Key in the amount of the initial investment, press Þ if that cash flow is negative, then press gJ. 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 75 Keystrokes Display 500ÞgK –500.00 Stores CF1 (with minus sign for a negative cash flow). 4500gK 4,500.00 Stores CF2. 5500gK 5,500.00 Stores CF3. 4500gK 4,500.00 Stores CF4. 130000gK 130,000.00 Stores CF5. :n 5.00 Checks number of cash flow amounts entered (in addition to CF0 ). 13¼ 13.00 Stores i. fl 212.18 NPV. Since NPV is positive, the investment would increase the financial value of the investor’s assets.
Section 4: Additional Financial Functions In summary, to enter the amounts of the cash flows and the number of times they occur consecutively: 1. Press fCLEARH to clear the financial and storage registers. 2. Key in the amount of the initial investment, press Þ if that cash flow is negative, then press gJ. 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.
Section 4: Additional Financial Functions 77 Keystrokes Display fCLEARH 0.00 Clears financial and storage registers. 79000ÞgJ –79,000.00 Initial investment (with minus sign for a negative cash flow). 14000gK 14,000.00 First cash flow amount. 11000gK 11,000.00 Next cash flow amount. 10000gK 10,000.00 Next cash flow amount. 3ga 3.00 Number of times this cash flow amount occurs consecutively. 9100gK 9,100.00 Next cash flow amount. 9000gK 9,000.00 Next cash flow amount. 2ga 2.
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. Note: Remember that the fL function may take a significant amount of time to produce an answer, during which the calculator displays running.
Section 4: Additional Financial Functions 79 Reviewing Cash Flow Entries z To display a single cash flow amount, press :, then key in the number of the register containing the cash flow amount to be displayed. Alternatively, store the number of that cash flow amount (that is, the value of j for the CFj desired) in the n register, then press :gK. z To review all the cash flow amounts, press :g K repeatedly.
Section 4: Additional Financial Functions To display all the cash flow amounts and the number of times they occur consecutively: Keystrokes Display :ga 1.00 N7 :gK 100,000.00 CF7 :ga 1.00 N6 :gK 4,500.00 CF6 :ga 2.00 N5 :gK 9,000.00 CF5 . . . . . . . . . :ga 1.00 N1 :gK 14,000.00 CF1 :ga 1.00 N0 :gK –79,000.00 CF0 7n 7.00 Resets the number in the n register to its original value. Changing Cash Flow Entries z To change a cash flow amount: 1.
Section 4: Additional Financial Functions 81 Note: If you change the number in the n register in order to change an Nj, 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). If this is not done, NPV and IRR calculations will give incorrect results. Example 1: With the cash flows now stored in the calculator, change CF2 from $11,000 to $9,000, then calculate the new NPV for a 13.5% return.
Section 4: Additional Financial Functions 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.* The fE and fS 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 83 In ALG mode, perform the steps listed for RPN mode above but replace the last step with the step below. Keystrokes (ALG mode) Display +~} 123.07 Total price, including accrued interest. 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.
Section 4: Additional Financial Functions Depreciation Calculations The hp 12c platinum enables you to calculate depreciation and the remaining depreciable value (book value minus salvage value) using the straight-line, sum-of-the-years-digits, and declining-balance methods. To do so with any of these methods: 1. Enter the original cost of the asset, using $. 2. Enter the salvage value of the asset, using M. If the salvage value is zero, press 0M. 3.
Section 4: Additional Financial Functions 85 Keystrokes Display ~ 3,100.00 Remaining depreciable value after second year. 3f# 1,440.00 Depreciation in third year. ~ 1,660.00 Remaining depreciable value after third year. To calculate depreciation and the remaining depreciable value when the acquisition date of the asset does not coincide with the beginning of the fiscal accounting year, refer to the procedures in Section 13.
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 87 The Display Status Indicators Nine indicators that appear along the bottom of the display signify the status of the calculator for certain operations. These status indicators are described elsewhere in this handbook where the relevant operation is discussed. 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.
Section 5: Additional Operating Features Several options are provided for controlling how numbers appear in the display. But regardless of which display format or how many displayed decimal places you specify, the number inside the calculator — which appears altered in the display — is not altered unless you use the B, !, V, Ý, or # functions. Standard Display Format. The number 14.87 now in your calculator is currently being displayed in the standard display format with two decimal places shown.
Section 5: Additional Operating Features 89 exponent is simply how many decimal places you would move the decimal point in the mantissa before writing down the number in standard format. If the exponent is negative (that is, there is a minus sign between it and the mantissa), the decimal point should be moved to the left; this occurs for any number less than 1.
Section 5: Additional Operating Features Special Displays Running. Certain functions and many programs may take several seconds or more to produce an answer. During these calculations, the word running flashes in the display to let you know that the calculator is running. Overflow and Underflow. If a calculation results in a number whose magnitude is greater than 9.999999999 ×1099, the calculation is halted and the calculator displays 9.999999 99 (if the number is positive) or –9.
Section 5: Additional Operating Features 91 The ~ key is also useful for checking the first number entered to make sure you keyed it in correctly. Before pressing the operation key or equals key, however, you should press ~ again to return the second number entered to the display. Regardless of how many times you press ~, the calculator considers the number in the display to be the second number entered.
Section 5: Additional Operating Features Recovering From Errors in Digit Entry Example: Suppose you want to divide the total annual production for one of your firm’s products (429,000) by the number of retail outlets (987) in order to calculate the average number distributed by each outlet. Unfortunately, you mistakenly key in the number of outlets as 9987 rather than as 987. It’s easy to correct: Keystrokes (RPN mode) Display 429000\ 429,000.00 9987 9,987. You haven’t noticed your mistake yet.
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 The table below shows where the accumulated statistics are stored. Register R1 (and display) Statistic n: number of data pairs accumulated. R2 Σx: summation of x-values. R3 Σx : summation of squares of x-values. R4 Σy: summation of y-values. R5 Σy summation of squares of y-values. R6 Σxy: summation of products of x-values and y-values.
Section 6: Statistics Functions Salesperson Hours/Week Sales/Month 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 95 To find the average workweek and sales of this sample: Keystrokes Display fCLEAR² 0.00 Clears statistics registers. 32\ 17000_ 32.00 1.00 First entry. 40\ 25000_ 40.00 2.00 Second entry. 45\ 26000_ 45.00 3.00 Third entry. 40\ 20000_ 40.00 4.00 Fourth entry. 38\ 21000_ 38.00 5.00 Fifth entry.
Section 6: Statistics Functions Standard Deviation Pressing gv calculates the standard deviation of the x-values (sx) and of the y-values (sy). (The standard deviation of a set of data is a measure of the dispersion around the mean.) The standard deviation of the x-values appears in the display after gv is pressed; to display the standard deviation of the y-values, press ~.
Section 6: Statistics Functions 97 To continue summing data pairs, press gÖg^ before entering more data. Note: In some cases involving data values that differ by a relatively small amount, the calculator cannot compute the standard deviation or the linear estimation accurately because such calculations would exceed the precision of the calculator.
Section 6: Statistics Functions Example: Check the reliability of the linear estimate in the preceding example by displaying the correlation coefficient. Keystrokes Display ~ 0.90 The correlation coefficient is close to 1, so the sales calculated in the preceding example is a good estimate. To graph the regression line, calculate the coefficients of the linear equation y = A + Bx. 1. Press 0gR to compute the y-intercept (A). 2. To compute the slope of the line (B) in RPN mode, press 1gR~d~-.
Section 6: Statistics Functions 99 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 101 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. In RPN mode, the original number can be recalled to the display by pressing gF. Fractional.
Section 7: Mathematics and Number-Alteration Functions The Power Function in RPN Mode 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.
Part II Programming File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 103 of 275 Printed Date: 2005/8/1 Dimension: 14.
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 105 Example: Your office supplies dealer is selling selected stock at 25% off. Create a program that calculates the net cost of an item after the discount is subtracted and the $5 handling charge is added. First, we’ll manually calculate the net cost of an item listing for $200. Keystrokes (RPN mode) Display 200 200. Keys in cost of item. \ 200.00 Separates cost of item from percentage to be keyed in next. 25b 50.00 Amount of discount. - 150.
Section 8: Programming Basics Keystrokes (RPN mode) Display \ 001, 36 2 002, 2 5 003, 5 b 004, 25 - 005, 30 5 006, 5 + 007, 40 Keystrokes (ALG mode) Display - 001, 30 2 002, 2 5 003, 5 b 004, 25 + 005, 40 5 006, 5 } 007, 36 Running a Program To run (sometimes called “execute”) a program: 1. Press fs to set the calculator back to Run mode. If the calculator is already in Run mode (that is, the PRGM status indicator in the display is not lit), skip this step.
Section 8: Programming Basics 107 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 Sets calculator to Run mode. Display shows number previously calculated. f] 155.00 Sets RPN mode. 625 625. Keys in price of typewriter. t 473.75 Net cost of typewriter. 159 159. Keys in list price of chair. t 124.25 Net cost of chair. Keystrokes (ALG mode) Display fs 155.
Section 8: Programming Basics Program Memory Keystrokes entered into the calculator in Program mode are stored in program memory. Each digit, decimal point, or function key is called an instruction and is stored in one line of program memory — usually referred to simply as a program line. Keystroke sequences beginning with the f, g, ?, :, and i prefix keys are considered to comprise a complete instruction and are stored in only one program line.
Section 8: Programming Basics 109 Since keystroke sequences beginning with f, g, ?, :, and i are stored in only one program line, the display of that line would show the keycodes for all the keys in the keystroke sequence. Instruction Keycode gÒ nnn, 43 26 ?=0 nnn, 44 40 0 gi000 nnn,43,33,000 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.
Section 8: Programming Basics For example, to display the first two lines of the program now stored in program memory, set the calculator to Program mode and press Ê twice: Keystrokes (RPN mode) Display fs 000, Ê 001, 36 Ê 002, 2 Keystrokes (ALG mode) Display fs 000, Ê 001, 30 Ê 002, 2 Sets calculator to Program mode and displays current line of program memory Program line 001: \ Program line 002: digit 2.
Section 8: Programming Basics 111 If either the Ê key or the Ü key is held down, the calculator displays all of the lines in program memory. Press Ê again now, but this time hold it down until program line 007 is displayed. Keystrokes (RPN mode) Display Ê 001, 36 . . . (Release Ê) 007, Keystrokes (ALG mode) Display Ê 001, . . . 40 Program line 007 30 Program line 001 . . . (Release Ê) 007, Program line 001 . . .
Section 8: Programming Basics The 000 Instruction and Program Line 000 Whenever you run the program now stored in program memory, the calculator executes the instruction in line 008 after executing the seven instructions you keyed in. This i000 instruction — as its name implies — tells the calculator to “go to” program line 000 and execute the instruction in that line.
Section 8: Programming Basics 113 To determine at any time how many program lines (including those containing gi000) are currently in program memory, press gN (memory). The calculator will respond with a display like the following: If you find yourself creating long programs, you should create your programs so that they don’t use up program lines unnecessarily, since program memory is limited to 400 program lines.
Section 8: Programming Basics Setting the Calculator to a Particular Program Line There will be occasions when you’ll want to set the calculator directly to a particular program line — such as when you’re storing a second program in program memory or when you’re modifying an existing program. Although you can set the calculator to any line by using Ç as described above, you can do so more quickly as follows: z With the calculator in Program mode, pressing gi.
Section 8: Programming Basics 115 Keystrokes (RPN mode) Display fs 124.25 Sets calculator to Run mode and to line 000 in program memory. (Display shown assumes results remain from previous calculation.) 625 625. Keys in price of typewriter. Ç 001, 625.00 Ç 002, 2. Ç 003, 25. Ç 004, 156.25 Ç 005, 468.75 Ç 006, 5. Ç 007, 473.75 36 Program line 001: \ Result of executing program line 001. 2 Program line 002: 2. Result of executing program line 002. 5 Program line 003: 5.
Section 8: Programming Basics Keystrokes (ALG mode) Display fs 124.25 Sets calculator to Run mode and to line 000 in program memory. (Display shown assumes results remain from previous calculation.) 625 625. Keys in price of typewriter. Ç 001, 625.00 Ç 002, 2. Ç 003, 25. Ç 004, 156.25 Ç 005, 468.75 Ç 006, 5. Ç 007, 473.75 30 Program line 001: Result of executing program line 001. 2 Program line 002: 2. Result of executing program line 002. 5 Program line 003: 5.
Section 8: Programming Basics 117 Interrupting Program Execution Occasionally you’ll want a program to stop executing so that you can see an intermediate result or enter new data. The hp 12c platinum provides two functions for doing so: gu (pause) and t (run/stop). Pausing During Program Execution When a running program executes a gu instruction, program execution halts for about 1 second, then resumes.
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 gu instructions in the program so that the intermediate results AMOUNT and TAX are automatically displayed when the program is executed. Keystrokes (RPN mode) Display 6.75?0 6.75 Stores tax rate in R0. fCLEAR² 0.00 Clears the registers in R1 through R6. 13 13.
Section 8: Programming Basics 119 Keystrokes (RPN mode) Display § 890.50 AMOUNT. ?+1 890.50 Adds AMOUNT to sum of AMOUNT entries in register R1. :0 6.75 Recalls tax rate to display. b 60.11 TAX. ?+2 60.11 Adds TAX to sum of TAX entries in register R2. + 950.61 TOTAL. ?+3 950.61 Adds TOTAL to sum of TOTAL entries in register R3. Keystrokes (ALG mode) Display 6.75?0 6.75 Stores tax rate in R0. fCLEAR² 0.00 Clears the registers in R1 through R6. 13 13.
Section 8: Programming Basics Now, we’ll store the program in program memory. Do not key in the quantity and cost of each item; these numbers will vary each time the program is run. Keystrokes (RPN mode) Display fs Sets calculator to Program mode. fCLEARÎ 000, § 001, gu 002, ?+1 003, 44 40 1 :0 004, 0 b 005, gu 006, ?+2 007, 44 40 + 008, ?+3 009, 44 40 Keystrokes (ALG mode) Display Clears program memory. 20 43 45 31 Pauses to display AMOUNT.
Section 8: Programming Basics Keystrokes (ALG mode) Display ?+3 012, 44 40 121 3 Note: The procedure used in the ALG program in steps 1 through 3 allows the algebraic program to run in the same manner as the RPN version. In the instructions below, the \ key is the same as the } key in ALG mode. Now, to run the program, first set the appropriate mode by pressing f] or f[ and then do the following: Keystrokes Display fs 950.61 Sets calculator to Run mode. fCLEAR² 0.00 Clears registers R1– R6.
Section 8: Programming Basics Keystrokes Display :2 402.82 Sum of TAX column. :3 6,370.52 Sum of TOTAL column. 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 gu instruction. Alternatively, you can have the program automatically stop as described next. Stopping Program Execution Stopping Program Execution Automatically. Program execution is automatically halted when the program executes a t instruction.
Section 8: Programming Basics 123 Keystrokes (ALG mode) Display § 001, 20 ~ 002, 34 } 003, 36 t 004, 31 Stops program execution to display AMOUNT. ?+1 005, 44 40 = 006, :0 007, b 008, 25 t 009, 31 Stops program execution to display 1 40 45 0 TAX. ?+2 010, 44 40 } 011, ?+3 012, 44 40 2 36 3 Now, to run the program, first set the appropriate mode by pressing f] or f[ and then do the following: Keystrokes Display fs 6,370.52 Sets calculator to Run mode. fCLEAR² 0.
Section 8: Programming Basics Keystrokes Display t 137.70 TAX for third item. t 2,177.70 TOTAL for third item. 5\345 345. Fourth item. t 1,725.00 AMOUNT for fourth item. t 116.44 TAX for fourth item. t 1,841.44 TOTAL for fourth item. :1 5,967.70 Sum of AMOUNT column. :2 402.82 Sum of TAX column. :3 6,370.52 Sum of TOTAL column.
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 Looping If a i instruction specifies a lower-numbered line in program memory, the instructions in the program lines between the specified line and the i instruction will be executed repeatedly. As can be seen in the illustration above under Simple Branching, once the program begins executing the “loop” it will execute it again and again.
Section 9: Branching and Looping Keystrokes Display f! 003, 42 11 Amortizes payment(s). gu 004, 43 31 Pauses to display amount of 127 payment(s) applied to interest. ~ 005, 34 Brings amount of payment(s) applied to principal into “display.”* gu 006, 43 31 Pauses to display amount of payment(s) applied to principal.
Section 9: Branching and Looping Keystrokes Display –593.75 Ê 004, Portion of first month’s payment applied to interest. 43 31 Line 004: gu. –593.75 Ê 34 Line 005: ~. 005, –188.72 Ê 006, Portion of first month’s payment applied to principal. 43 31 Line 006: gu. –188.72 Ê 007,43, 33,002 Line 007: gi002. This is the end of the first pass through the loop. –188.72 Ê 002, 45 0 Line 002: :0. Program execution has branched to the beginning of the loop for the second pass through it. 1.
Section 9: Branching and Looping 129 Keystrokes Display t –592.25 Portion of third month’s payment applied to interest. –190.22 Portion of third month’s payment applied to principal. –190.22 Halts program execution. t(or any key) Conditional Branching Often there are situations when it is desirable for a program to be able to branch to different lines in program memory, depending on certain conditions.
Section 9: Branching and Looping These rules can be summarized as “DO if TRUE”. The program line immediately following that containing the conditional test instruction can contain any instruction; however, the most commonly used instruction there is i. If a i instruction follows a conditional test instruction, program execution branches elsewhere in program memory if the condition is true and continues with the next line in program memory if the condition is false.
Section 9: Branching and Looping 131 RPN program notes: We’ll key the income into the display before running the program so that it will be in the X-register when the :0 instruction in program line 001 is executed. This instruction will place the test value 20,000 in the X-register and (as explained in Appendix A) move the income into the Y-register.
Section 9: Branching and Looping Keystrokes (RPN mode) Display go 003, gi007 004,43, 33,007 If condition is true, branches to program line 007. :2 005, If condition is false, recalls 25% tax rate to X-register. gi008 006,43, 33,008 Branches to program line 008. :1 007, Recalls 20% tax rate to X-register. b 008, fs –190.22 43 45 45 34 2 1 25 Tests whether number in X-register (income) is less than or equal to number in Y-register (20,000). Calculates tax.
Section 9: Branching and Looping 133 Keystrokes (ALG mode) Display :0 002, ~ 003, 34 Places income in X-register and test value in Y-register. § 004, 20 Prepares for multiplication. go 005, 34 Tests whether number in X-register (income) is less than or equal to number in Y-register (20,000). gi009 006,43, 33,009 If condition is true, branches to program line 009. :2 007, If condition is false, recalls 25% tax rate to X-register. gi010 008,43, 33,010 Branches to program line 010.
Section 9: Branching and Looping Keystrokes (RPN mode) Display 20,000.00 Ê Test value has been recalled to X-register, moving income to Y-register. 34 Line 002: ~ 002, 15,000.00 Ê 003, 43 Income has been placed in X-register and test value has been placed in Y-register. 34 Line 003: go 15,000.00 Ê 004,43,33,007 Condition tested by o was true, so program execution continued with line 004: gi007. 15,000.00 Ê 007, 45 1 Line 007: :1. 20.
Section 9: Branching and Looping 135 Keystrokes (RPN mode) Display Ê 004,43, 33,007 Condition tested by o was true, so program execution continued with line 004: gi007. 20,000.00 Ê 007, 45 20.00 Ê 1 Line 007: :1. 20% tax rate has been recalled to X-register, moving income to Y-register. 25 Line 008: b. 008, 4,000.00 20% of 20,000 = 4,000. 25000 25,000. Keys income greater than test value into display and X-register. Ê 001, 45 20,000.
Section 9: Branching and Looping Keystrokes (ALG mode) Display 20000?0 20,000.00 Stores test value in register R0. 20?1 20.00 Stores 20% tax rate in register R1. 25?2 25.00 Stores 25% tax rate in register R2. 15000 15,000. Keys income less than test value into display and X-register. Ê 001, 44 9 Line 001: ?9. 15,000.00 Ê 002, 45 Stores income into register R9. 0 Line 002: :0. 20,000.00 Ê Test value has been recalled to X-register, moving income to Y-register.
Section 9: Branching and Looping Keystrokes (ALG mode) Display Ê 012,43,33,000 Line 012: gi000. 137 3,000.00 20000 20,000. Ê 001, Keys income equal to test value into display and X-register. 44 20,000.00 Ê 002, 45 20,000.00 Ê Stores income into register R9. 0 Line 002: :0. Test value has been recalled to X-register, moving income to Y-register. 34 Line 003: ~. 003, 20,000.00 Ê 9 Line 001: ?9. Income has been placed in X-register and test value has been placed in Y-register.
Section 9: Branching and Looping Keystrokes (ALG mode) Display 25000 25,000. Ê 001, Keys income greater than test value into display and X-register. 44 9 Line 001: ?9. 25,000.00 Ê 002, 45 Stores income into register R9. 0 Line 002: :0. 20,000.00 Ê Test value has been recalled to X-register, moving income to Y-register. 34 Line 003: ~. 003, 25,000.00 Ê Income has been placed in X-register and test value has been placed in Y-register. 20 Line 004: §. 004, 25,000.
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 Keystrokes (RPN mode) Display Ê 006,43, 33,008 Shows that instruction in program line 006 has not been changed. fs 6,250.00 Sets calculator back to Run mode. (Display shown assumes results remain from last example in preceding section.) :2?6 25.00 Copies tax rate from R2 into R6. Keystrokes (ALG mode) Display fs Sets calculator to Program mode. gi.006 006,43, 33,009 Sets calculator to program line preceding that containing the instruction to be changed.
Section 10: Program Editing 141 Note: To add one or more instructions at the end of a program that is not the last program stored in program memory, use the procedure described below under Adding Instructions within a Program. Example: With the last program from the preceding section stored in the calculator, suppose you wanted to calculate the net income after taxes. In the RPN program, you could add a - instruction at the end in order to calculate the net income after taxes.
Section 10: Program Editing Keystrokes (ALG mode) Display 15000t 12,000.00 Net income after 20% tax is subtracted from $15,000 income. 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 143 4. Key in the original instruction or instructions, beginning with the first instruction to be executed after the added instruction(s), and continuing through the last instruction you keyed into program memory.
Section 10: Program Editing Keystrokes (ALG mode) Display Þ 013, 16 Keys new instruction into program line 013. + 014, 40 Keys new instruction into program line 014. :9 015, 9 Keys new instruction into program line 015. } 016, 36 Keys new instruction into program line 016. fs 12,000.00 Sets calculator back to Run mode. 15000t 3,000.00 Twenty percent tax on $15,000 income. t 12,000.00 Net income after 20% tax is subtracted from $15,000 income.
Section 10: Program Editing 145 ensures that program execution will branch to line 000 after the program is run. 6. Key in the instruction(s) being added. 7. Key in the instruction that originally immediately followed the point at which the new instruction(s) are being added — that is, the first instruction to be executed after the added instruction(s). (This instruction was replaced by the i instruction keyed in at step 3.) 8.
Section 10: Program Editing Keystrokes (RPN mode) Display :3 012, ~ 013, go 014, 45 3 34 43 34 Added instructions. gi000 015,43, 33,000 :0 016, 0 Keys in instruction immediately following point at which new instructions are being added. (This instruction was replaced in line 001 by gi012 instruction.) gi002 017,43, 33,002 Branches back to second line (line 002) following point at which new instructions are being added. fs 12,000.00 Sets calculator back to Run mode.
Section 10: Program Editing 147 Keystrokes (ALG mode) Display gi018 001,43, 33,018 Branches to program line 018, the second line after last line of program. gi.016 016, Sets calculator to last line of program so that the gi000 instruction keyed in next will be stored as the last line of the current program. gi000 017,43, 33,000 :3 018, ~ 019, go 020, gi000 021,43, 33,000 ?9 022, 9 Keys in instruction immediately following point at which new instructions are being added.
Section 10: Program Editing The following illustration of the edited RPN program shows how program execution branches to the instructions added at the end of program memory, then branches back. While the actual program in ALG mode is different, the illustration does indicate the method used. File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 148 of 275 Printed Date: 2005/8/1 Dimension: 14.
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 in RPN mode and 23 program lines in ALG mode), store after that program the office-supplies program from Section 8 (page 104). 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 151 Keystrokes (ALG mode) Display - 025, 30 2 026, 2 5 027, 5 b 028, 25 + 029, 40 5 030, 5 } 031, 36 t 032, 31 gi025 033,43, 33,025 Branches to beginning of program. fs 12,000.00 Sets calculator back to Run mode. (Display shown assumes results remain from running program in previous example.) Keys in program. Halts program execution.
Section 11: Multiple Programs Keystrokes (RPN mode) Display ?0 028, 44 0 :0 029, 45 0 f! 030, 42 11 gu 031, 43 31 ~ 032, gu 033, gi029 034,43, 33,029 Keystrokes (ALG mode) Display 43 31 fs gi.033 Keys in program 34 Sets calculator to Program mode. 033,43, 33,025 Sets calculator to last line keyed into program memory.
Section 11: Multiple Programs 153 Running Another Program To run a program that does not begin with program line 001: 1. Press fs to set the calculator to Run mode. If the calculator is already in Run mode, skip this step. 2. Press gi followed by three digits that specify the first line of the program. 3. Press t. Example: Run the office-supplies program, now stored in the calculator beginning at program line 019 in RPN mode and line 025 in ALG mode, for the typewriter listing for $625.
Part III Solutions File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 155 of 275 Printed Date: 2005/8/1 Dimension: 14.
Section 12 Real Estate and Lending Annual Percentage Rate Calculations With Fees Borrowers are usually charged fees in connection with the issuance of a mortgage, which effectively raises the interest rate. The actual amount received by the borrower (PV) is reduced, while the periodic payments remain the same. Given the life or term of the mortgage, the interest rate, the mortgage amount, and the basis of the fee charge (how the fee is calculated), the true Annual Percentage Rate (APR) may be calculated.
Section 12: Real Estate and Lending 157 ALG Mode: z If fees are stated as a percentage of the mortgage amount (points), recall the mortgage amount (:$); press -; key in the fee (percentage) rate; press b$. z If fees are stated as a flat charge, recall the mortgage amount (:$); press -; key in the fee amount (flat charge); press $.
Section 12: Real Estate and Lending Example 2: Using the same information as given in example 1, calculate the APR if the mortgage fee is $750 instead of a percentage. Keystrokes (RPN mode) Keystrokes (ALG mode) f] f[ g g fCLEARG fCLEARG 30gA 30gA 360.00 Months (into n) 5.5gC 5.5gC 0.46 Percent monthly interest rate (into i). 160000$ 160000$ 160,000.00 Loan amount (into PV). P P –908.46 Monthly payment (calculated). :$750$ :$-750 $ 159,250.00 ¼ ¼ 0.
Section 12: Real Estate and Lending 159 Keystrokes (RPN mode) Keystrokes (ALG mode) Display ¼ ¼ 0.48 Monthly interest rate (calculated). 12§ §12³ 5.73 Annual percentage rate. Price of a Mortgage Traded at a Discount or Premium Mortgages may be bought and/or sold at prices lower (discounted) or higher (at a premium) than the remaining balance of the loan at the time of purchase.
Section 12: Real Estate and Lending Keystrokes (RPN mode) Keystrokes (ALG mode) Display 9gC 9gC 0.75 Discount rate (into i). 137.17P* 137.17P* 137.17 Monthly payments (into PMT). 2000M$ 2000M$ –8,777.61 Amount necessary to prepay the note. Example 2: A 6.5% mortgage with 26 years remaining and a remaining balance of $249,350 is available for purchase. Determine the price to pay for this mortgage if the desired yield is 12%. (Since the payment amount is not given, it must be calculated.
Section 12: Real Estate and Lending 161 Yield of a Mortgage Traded at a Discount or Premium The annual yield of a mortgage bought at a discount or premium can be calculated given the original mortgage amount, interest rate, and periodic payment, as well as the number of payment periods per year, the price paid for the mortgage, and the balloon payment amount (if it exists). Information is entered as follows: 1. Press g and fCLEARG. 2.
Section 12: Real Estate and Lending Keystrokes (RPN mode) Keystrokes (ALG mode) Display P P 2,096.57 Payment received (calculated). :n :n 252.00 Recall number of periods. 42-n -42n 210.00 Number of periods left after mortgage is bought (into n). 250000Þ$ 250000Þ$ –250,000.00 Input price of mortgage (into PV; negative to indicate money paid out). ¼ ¼ 0.60 Yield per month (calculated). 12§ §12³ 7.20 Percent annual yield.
Section 12: Real Estate and Lending 163 Calculate the remaining balance of the loan after five years. Keystrokes (RPN mode) Keystrokes (ALG mode) Display 5gA 5gA 60.00 Number of periods to be amortized. M M 258,377.24 Remaining balance of the loan after five years. :n :n 60.00 42-n -42n 18.00 250000Þ$ 250000Þ$ 1.01 ¼ ¼ 12§ §12³ 12.11 New life of loan. Percent monthly yield. (calculated). Percent annual yield.
Section 12: Real Estate and Lending KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY fCLEARÎ 000, M 001, M* DISPLAY fCLEARÎ 000, 15 M 001, 15 002, 15 M* 002, 15 Þ 003, 16 Þ 003, 16 ?.1 004,44 48 ?.
Section 12: Real Estate and Lending KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY § 022, f! 023, Þ 024, :n 025, z 026, :4 027, + 028, :.0 029,45 48 b 030, :4 031, - 032, :5 033, - 034, :8 035, + 036, :P 037, + 165 DISPLAY 20 2 022, 11 f! 023, 16 Þ 024, 16 11 z 025, 10 10 :n 026, + 027, :4 028, § 029, :.
Section 12: Real Estate and Lending KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY DISPLAY M 046, 15 :$ 046, t 047, 31 M 047, 15 :1 048, 45 1 t 048, 31 :6 049, 45 6 :1 049, + 050, 40 Þ 050, 16 Þ 051, 16 - 051, 30 $ 052, 13 :6 052, ¼ 053, 12 $ 053, 13 :gC 054,45, 43 12 ¼ 054, 12 t 055, 31 :gC 055,45, 43 12 :9 056, 45 9 t 056, 31 gC 057, 43 12 :9 057, 45 9 M 058, 15 gC 058, 43 12 M 059, fs 45 45 45 fs REGISTE
Section 12: Real Estate and Lending 167 1. Key in the program. 2. Key in the estimated down payment then press ?1. 3. Key in the life of the mortgage then press ?2. 4. Key in the annual mortgage interest rate then press ?3. 5. Key in the estimated monthly taxes then press ?4. 6. Key in the total amount estimated for monthly repairs, improvements, incremental insurance, utility costs, and other expenses, then press ?5. 7. Key in the closing costs then press ?6. 8.
Section 12: Real Estate and Lending Example: You are being transferred for 4 years to a distant city and are faced with the decision of whether to rent or to buy a house. A quick survey of the housing market indicates that you can purchase an acceptable house for $270,000 with a $7,000 down payment on a 30-year mortgage at 6% interest. The closing costs would be about $3,700. Selling costs include a 6% commission for resale and miscellaneous other fees that amount to another 2% of the sale price.
Section 12: Real Estate and Lending Keystrokes (RPN mode) Keystrokes (ALG mode) Display t t 8.57 Yield. t t 46,048.61 Balance in savings. 169 By purchasing a house, you would gain $7,047.04 (53,095.65 – 46,048.61) over an alternate investment at 3% interest. Deferred Annuities Sometimes transactions are established where payments do not begin for a specified number of periods; the payments are deferred. The technique for calculating NPV may be applied assuming zero for the first cash flow.
Section 12: Real Estate and Lending In the example cited, the rental payment stream for months 7 through 24 are “deferred annuities,” as they start at some time in the future. The cash flow diagram from the investor’s viewpoint looks like this: To find today’s present value of the cash flows assuming a desired yield, the NPV technique may be used. (Refer to pages 73 through 77.
Section 13 Investment Analysis Partial-Year Depreciation For both income tax purposes and financial analyses, it is valuable to calculate depreciation based on a calendar or fiscal accounting year. When the acquisition date of an asset does not coincide with the start of the year — which is the rule rather than the exception — the amounts of depreciation in the first and last years are computed as fractions of a full year’s depreciation.
Section 13: Investment Analysis KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY :1 012, 45 1 § 013, ?3 014, 44 3 :$ 015, 45 ~ DISPLAY 1 012, fV 013, § 014, 13 :1 015, 016, 34 ³ 016, - 017, 30 ?3 017, 44 3 $ 018, 13 :$ 018, 45 13 :n 019, 45 11 - 019, 30 :1 020, 45 1 ~ 020, 34 - 021, 30 $ 021, 13 n 022, 11 :n 022, :0 023, 45 0 - 023, gm 024, 43 35 :1 024, gi035 025,43, 33, 035 n 025, :2 026, 45 2 :0 026, 45 0
Section 13: Investment Analysis KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY 173 DISPLAY gu 036, 43 31 ?=2 036,44 40 :$ 037, 45 13 gi029 037,43,33, 029 :M 038, 45 15 :2 038, 45 2 - 039, 30 gu 039, 43 31 :3 040, :$ 040, 45 13 gi030 041,43,33, 030 - 041, :M 042, ³ 043, :3 044, gi033 045,43,33, 033 45 3 fs 30 45 45 REGISTERS n: Life i: Unused PV: Dep. Value PMT: Unused FV: Salvage R0: Used R1: #Mos./12 R2: Counter st R4–R.4: Unused 1.
Section 13: Investment Analysis RPN Mode: 6. Key in the year desired then press \. 7. Key in the number of months in the first year and press t.* The display will show the amount of depreciation for the desired year. If desired, press ~ to see the remaining depreciable value then press :$:3=~-:M- to find the total depreciation from the first year through the current year. ALG Mode: 6. Key in the year desired then press ³. 7. Key in the number of months in the first year and press t.
Section 13: Investment Analysis 175 Keystrokes (RPN mode) Keystrokes (ALG mode) f] f[ fCLEARG fCLEARG 125000$ 125000$ 125,000.00 Book value. 25n 25n 25.00 Life. 1\ 1³ 1.00 Year desired. 4t 4t ~ ~ 1.00 1,666.67 123,333.33 First year: depreciation, remaining depreciable value. t t ~ ~ 2.00 5,000.00 118,333.33 Second year: depreciation, remaining depreciable value. t t 3.00 5,000.00 Third year: depreciation. Display Salvage value = 0 so FV = 0; set to 0 by CLEARG.
Section 13: Investment Analysis Example 2: A used car was purchased for $6,730 with 4.5 months remaining in the year. If the expected life of the car is 5 years, what is the amount of depreciation in the first year? Keystrokes (RPN mode) Keystrokes (ALG mode) f] f[ gi000 fCLEARG gi000 fCLEARG 6730$ 6730$ 6,730.00 Book value. 5n 5n 5.00 Life. 1\ 1³ 1.00 4.5t 4.5t 1.00 504.75 Display First year: depreciation.
Section 13: Investment Analysis KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY 177 DISPLAY ³ 010, ?0 011, 1 012, f# 013, § 014, 13 :1 015, 016, 34 ³ 016, - 017, 30 ?3 017, 44 3 $ 018, 13 :$ 018, 45 13 :0 019, 45 0 - 019, 30 gm 020, 43 35 ~ 020, 34 gi031 021,43, 33, 031 $ 021, 13 :2 022, 45 2 :0 022, 45 0 gu 023, 43 31 gm 023, 43 35 :0 024, 45 0 gi034 024,43, 33, 034 f# 025, 42 25 :2 025, 45 2 t 026, 31 gu 026, 43
Section 13: Investment Analysis KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY :M 034, - 035, :3 036, gi026 037,43,33, 026 45 45 15 :2 034, 45 2 30 gu 035, 43 31 :$ 036, 45 13 - 037, :M 038, ³ 039, :3 040, gi029 041,43,33, 029 3 fs DISPLAY 30 45 36 45 fs REGISTERS n: Life i: Factor PV: Dep. Value PMT: Unused FV: Salvage R0: Used R1: #Mos./12 R2: Counter st R3:1 Yr. Dep. 15 R4–R.4: Unused 1. Key in the program. 2. Press fCLEARG. 3.
Section 13: Investment Analysis 179 RPN Mode: 7. Key in the year desired then press \. 8. Key in the number of months in first year* and press t.† The display will show the amount of depreciation for the desired year. Press ~ to see the remaining depreciable value. If desired, press :$:3=~-:M- to find the total depreciation through the current year. ALG Mode: 7. Key in the year desired then press ³. 8. Key in the number of months in first year* and press t.
Section 13: Investment Analysis Keystrokes (RPN mode) Keystrokes (ALG mode) Display 11,458.33 depreciation. Sum-of-the-Years-Digits Depreciation The following hp 12c platinum program 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 KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY $ 018, :n 019, :1 020, - 181 DISPLAY 13 :$ 018, 45 11 - 019, 30 45 1 ~ 020, 34 021, 30 $ 021, 13 n 022, 11 :n 022, :0 023, 45 0 - 023, gm 024, 43 35 :1 024, gi035 025,43,33, 035 n 025, :2 026, 45 2 :0 026, 45 0 gu 027, 43 31 gm 027, 43 35 :0 028, 45 0 gi038 028,43,33, 038 fÝ 029, 42 24 :2 029, 45 2 t 030, 31 gu 030, 43 31 1 031, 1 :0
Section 13: Investment Analysis KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY fs DISPLAY :M 042, ³ 043, :3 044, gi033 045,43,33, 033 45 36 45 fs REGISTERS n: Life i: Unused PV: Dep. Value PMT: Unused FV: Salvage R0: Used R1: #Mos./12 R2: Counter st R3: 1 Yr. Dep. 15 R4–R.4: Unused 1. Key in the program. 2. Press fCLEARG. 3. Key in the book value then press $. 4. Key in the salvage value then press M. 5. Key in the life in years (an integer) then press n.
Section 13: Investment Analysis 183 RPN Mode: 6. Key in the year desired then press \. 7. Key in the number of months in first year* then press t.† The display will show the amount of depreciation for the desired year. If desired, press ~ to see the remaining depreciable value, then press :$:3=~-:M- to find the total depreciation through the current year. ALG Mode: 6. Key in the year desired then press ³. 7. Key in the number of months in first year* then press t.
Section 13: Investment Analysis Keystrokes (RPN mode) Keystrokes (ALG mode) 11t 11t ~ ~ t t ~ ~ Display 4.00 781.41 8,238.71 Fourth year: depreciation, remaining depreciable value. 5.00 746.02 7,492.69 Fifth year: depreciation, remaining depreciable value. 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.
Section 13: Investment Analysis KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY 185 DISPLAY 4 ~ 008, 34 33 ³ 009, 36 0 ?4 010, 011, 1 d 011, 33 ?-0 012,44 30 0 d 012, 33 ?2 013, 44 2 ?0 013, ?3 014, 44 3 1 014, 1 f# 015, 42 25 ?-0 015,44 30 0 :6 016, 45 6 ?2 016, 44 2 § 017, 20 ?3 017, 44 3 ?1 018, 44 1 f# 018, 42 25 :$ 019, 45 13 § 019, ~ 020, 34 :6 020, - 021, 30 ³ 021, $ 022, 13 ?1 022, 44 1 \ 023, 36 :$
Section 13: Investment Analysis KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY DISPLAY gi039 032,43,33, 039 ~ 032, d 033, 33 :0 033, d 034, 33 1 034, 1 035, 1 go 035, gu 036, 31 gi043 036,43,33, 043 d 037, 33 d 037, 33 t 038, 31 d 038, 33 1 039, 1 1 039, 1 ?+2 040,44 40 2 gu 040, ?-0 041,44 30 0 d 041, 33 f# 042, 42 25 t 042, 31 ?+1 043,44 40 1 1 043, 1 ?5 044, 44 5 ?+2 044,44 40 2 :$ 045, 45 13 ?-0 045,44 30 0 :M
Section 13: Investment Analysis KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY 187 DISPLAY go 056, 34 gi058 056,43,33, 058 gi086 057,43,33, 086 gi070 057,43,33, 070 :$ 058, 45 13 d 058, 33 :5 059, 45 5 0 059, 0 - 060, 30 :0 060, 45 0 $ 061, 13 go 061, 43 34 1 062, 1 gi091 062,43,33, 091 ?-4 063,44 30 4 :$ 063, gi040 064,43,33, 040 - 064, :4 065, :5 065, n 066, 11 $ 066, 13 0 067, 0 1 067, 1 ?6 068, 6 ?-4 068,44 30 4 1 069,
Section 13: Investment Analysis KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY DISPLAY fV 080, 42 23 ?+1 081,44 40 1 0 1 082, 1 1 ?-0 083,44 30 0 34 ?+2 084,44 40 2 gi074 085,43,33, 074 ?+3 085,44 40 3 d 086, 33 d 086, d 087, 33 :0 087, :2 088, 45 2 1 088, gu 089, 43 31 go 089, d 090, 33 gi079 090,43,33, 079 t 091, 31 d 091, 33 :6 092, 45 6 d 092, 33 gm 093, 43 35 :2 093, 45 2 gi074 094,43,33, 074 gu 094, 43 31 gi058
Section 13: Investment Analysis 189 REGISTERS n: Life i: Factor PV: Dep. Value PMT: Unused FV: Salvage R0: Used R1: Dep. R2: Counter R3: Used R4: Used R5: Used R6: Used 1. Key in the program. 2. Press fCLEARH. 3. Key in the book value then press $. 4. Key in the salvage value then press M. 5. Key in the life in years (an integer) then press n. 6. Key in the declining-balance factor as a percentage then press ¼. 7. RPN: Key in the desired year and press \. 7.
Section 13: Investment Analysis Keystrokes (RPN mode) Keystrokes (ALG mode) Display 500M 500M 500.00 Salvage value. 8n 8n 8.00 Life. 200¼ 200¼ 200.00 Declining-balance factor. 1\ 1³ 1.00 First year depreciation desired. 6t 6t ~ ~ 1.00 1,375.00 9,125.00 First year: depreciation, remaining depreciable value. t t 2.00 2,406.25 Second year: depreciation. t t 3.00 1,804.69 Third year: depreciation. t t 4.00 1,353.51 Fourth year: depreciation. t t 5.00 1,015.
Section 13: Investment Analysis 191 Excess Depreciation When accelerated depreciation is used, the difference between total depreciation charged over a given period of time and the total amount that would have been charged under straight-line depreciation is called excess depreciation. To obtain excess depreciation: RPN Mode: 1. Calculate the total depreciation then press \. 2. Key in the depreciable amount (cost less salvage) then press \. Key in the useful life of the asset in years then press z.
Section 13: Investment Analysis Modified Internal Rate of Return The traditional Internal Rate of Return (IRR) technique has several drawbacks which hamper its usefulness in some investment applications. The technique implicitly assumes that all cash flows are either reinvested or discounted at the computed yield rate. This assumption is financially reasonable as long as the rate is within a realistic borrowing and lending range (for example, 10% to 20%).
Section 13: Investment Analysis 193 Example: An investor has the following unconventional investment opportunity. The cash flows are: Group # of Months Cash Flow ($) 0 1 –180,000 1 5 100,000 2 5 –100,000 3 9 0 4 1 200,000 Calculate the MIRR using a safe rate of 6% and a reinvestment (risk) rate of 10%. Keystrokes (RPN mode) Keystrokes (ALG mode) f] f[ fCLEARH fCLEARH 0.00 0gJ 0gJ 0.00 100000gK 100000gK 100,000.00 5ga 5ga 5.00 Second through sixth cash flows.
Section 13: Investment Analysis Black-Scholes Formula for Valuing European Options This program implements the Black-Scholes formula which has been used extensively in option markets worldwide since its publication in the early 1970’s. The five inputs are simply keyed into the five financial variables and then t displays the call option value, and ~ shows the put option value. The option values produced are accurate to at least the nearest cent for asset and strike prices under $100.
Section 13: Investment Analysis KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY g° 017, ~ 195 DISPLAY 23 } 017, 018, 34 ?3 018, 44 3 z 019, 10 :$ 019, 45 13 gF 020, 40 z 020, 2 021, 2 :4 021, ?5 022, 5 } 022, z 023, 10 g° 023, + 024, 40 z 024, 10 ?6 025, 44 6 ~ 025, 34 :3 026, 45 3 } 026, 36 - 027, :3 027, ?3 028, z 028, 10 \ 029, 36 2 029, 2 § 030, 20 ?5 030, gr 031, 43 21 + 031, 40 gF 032, 43 40 ~ 032, 34
Section 13: Investment Analysis KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY DISPLAY 0 041, 0 } 041, 36 6 042, 6 Þ 042, 16 z 043, 10 g> 043, 43 22 1 044, 1 :3 044, 45 3 + 045, 40 g¡ 045, 43 20 y 046, 22 gr 046, 43 21 § 047, 20 z 047, 10 gF 048, 43 40 3 048, 3 gF 049, 43 40 .
Section 13: Investment Analysis KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY :3 065, ~ 066, ?3 067, O 45 3 197 DISPLAY :2 065, - 066, 30 3 2 067, 2 068, 35 4 068, 4 ~ 069, 34 § 069, 20 go 070, 34 :2 070, g(077 071,43,33,077 + 071, 40 1 072, 1 8 072, 8 ?-3 073,44 30 3 7 073, 7 Þ 074, § 074, 20 ?§3 075,44 20 ~ 075, 34 ~ 076, 34 § 076, 20 :5 077, 45 5 .
Section 13: Investment Analysis KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY ~ 089, :3 090, 45 3 :$ 091, 45 13 ?-4 092,44 30 4 § 093, :6 094, - 095, ?+4 096,44 40 :4 097, ~ 098, ?5 099, fs 34 ?-3 089,44 30 Þ 090, ?§3 091,44 20 ~ 092, :5 093, 45 5 gm 094, 43 35 g(106 095,43, 33, 106 4 :6 096, 45 6 4 :3 097, 45 3 § 098, :4 099, } 100, ?6 101, O 102, ?5 103, ~ 104, g(037 105,43, 33, 037 ~ 106, :$ 107, 45 13 ?-4 108,4
Section 13: Investment Analysis KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY 199 DISPLAY } 113, 36 ?+4 114,44 40 4 :4 115, 4 ~ 116, ?5 117, g(000 118,43,33, 000 45 34 44 5 fs REGISTERS n: Term to expiry i: Interest rate (%) PV: Stock price PMT: Volatility (%) FV: Strike price R0: Unused R1: Unused R2: Unused R3: N(d1) R4: Put value R5: Call value R6: QxN(d2) R7-R.
Section 13: Investment Analysis Example 1: An option has 6 months to run and a strike price of $45. Find Call and Put values assuming a spot price of $52, return volatility of 20.54% per month and a risk-free interest rate of 0.5% per month. Show how to change the time scale of the inputs between monthly and annual values. Keystrokes (RPN mode) Keystrokes (ALG mode) f] f[ 6n 6n 6.00 Time to expiry (months). .5¼ .5¼ 0.50 Interest rate (% per month). 52$ 52$ 52.00 Stock price. 20.54P 20.
Section 13: Investment Analysis 201 Example 2: The stock price six months from the expiration of an option is $42, the exercise price of the option is $40, the risk-free interest rate is 10% per annum, and the volatility is 20% per annum. Find Call and Put values. Keystrokes (RPN mode) Keystrokes (ALG mode) f] f[ .5n .5n 0.50 Time to expiry (years). 10¼ 10¼ 10.00 Interest rate (% per year). 42$ 42$ 42.00 Stock price. 20P 20P 20.00 Volatility (% per year). 40M 40M 40.00 Strike price.
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 203 Example 1: Equipment worth $750 is leased for 12 months. The equipment is assumed to have no salvage value at the end of the lease. The lessee has agreed to make three payments at the time of closing. What monthly payment is necessary to yield the lessor 10% annually? Keystrokes (RPN mode) Keystrokes (ALG mode) f] f[ g g fCLEARG fCLEARG 12\ 12- 12.00 Duration of lease. 3?0-n 3?0n 9.00 Number of periodic payments. 10gC 10gC 0.83 1ÞP 1ÞP –1.00 $:0+ $+:0³ 11.
Section 14: Leasing KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY ¼ 008, 12 1 009, 1 Þ 010, P DISPLAY ¼ 008, 12 1 009, 1 16 Þ 010, 16 011, 14 P 011, 14 $ 012, 13 $ 012, 13 :1 013, + 013, 40 + 014, :1 014, :3 015, ³ 015, ~ 016, 34 :3 016, z 017, 10 z 017, 10 ~ 018, 34 ³ 019, 36 45 1 40 45 3 fs 45 1 36 45 3 fs REGISTERS n: n–#Adv. Pmt. i: i PV: Used PMT: –1 FV: 0 R0: n R1: #Adv. Pmt. R2: i R3: Loan R4–R.7: Unused 1.
Section 14: Leasing 205 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) Keystrokes (ALG mode) f] f[ 12?0 12?0 12.00 Duration of lease. 3?1 3?1 3.00 Number of advance payments. 10\12z 10z12³ 0.83 ?2 ?2 0.83 Periodic interest rate. 750?3t 750?3t 64.45 Monthly payment to be received. 15\12z 15z12³ 1.25 ?2t ?2t 65.
Section 14: Leasing Solving for Yield To calculate the periodic yield, information is entered as follows: 1. Press g and fCLEARG. RPN Mode: 2. Key in the total number of payments in the lease then press \. 3. Key in the total number of payments made in advance then press ?0-n. 4. Key in the periodic payment to be received then press P. 5. Key in the total amount of the loan then press Þ:0:P§+$. 6. Press ¼ to obtain the periodic yield. ALG Mode: 2.
Section 14: Leasing Keystrokes (RPN mode) Keystrokes (ALG mode) Display ¼ ¼ 1.44 Monthly yield (calculated). 12§ §12³ 17.33 Annual yield (as a percentage).
Section 14: Leasing KEYSTROKES (RPN mode) :gC KEYSTROKES (ALG mode) DISPLAY 017,45,43 DISPLAY 12 fs REGISTERS n: n–#Adv. Pmts. i: i PV: Used PMT: Pmt. FV: 0 R0: n R1: Adv. Pmts. R2: Pmt. R3: Loan R4–R.7: Unused 1. 2. 3. 4. 5. Key in the program. Key in the total number of payments in the lease then press ?0. Key in the total number of payments made in advance then press ?1. Key in the periodic payment to be received then press ?2.
Section 14: Leasing 209 Advance Payments With Residual Situations may arise where a transaction has advance payments and a residual value (salvage value) at the end of the normal term. Solving for Payment The following program solves for the periodic payment amount necessary to achieve a desired yield.
Section 14: Leasing KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY n 018, 11 1 019, 1 Þ 020, P DISPLAY :4 018, n 019, 11 16 1 020, 1 021, 14 Þ 021, 16 $ 022, 13 P 022, 14 :4 023, 4 $ 023, 13 + 024, + 024, 40 :5 025, :4 025, ~ 026, 34 ³ 026, z 027, 10 :5 027, z 028, 10 ~ 029, 34 ³ 030, 36 45 40 45 5 fs 45 45 4 4 36 45 5 fs REGISTERS n: Used. i: Interest PV: Used PMT: –1. FV: Residual R0: # Pmts (n) R1: Interest.
Section 14: Leasing 211 7. For a new case, return to step 2. The values changed from the previous case are the only values which need to be re-entered. 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.
Section 14: Leasing Solving for Yield Solving for yield is essentially the same as solving for Internal Rate of Return (IRR). The keystrokes are as follows: 1. Press fCLEARH. 2. Key in the amount of the first cash flow then press gJ. This initial amount is the difference between the initial loan amount and any payments received at closing time. Observe the sign convention: positive for cash received and negative for cash paid out. 3. Key in the amount of the first cash flow then press gK.
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. RPN Mode: 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. Press ÞPM to obtain the effective annual interest rate. ALG Mode: 2. Key in the annual nominal rate as a percentage. 3. Press z.
Section 15: Savings For repeated calculations, the following hp 12c platinum program can be used: KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY fs DISPLAY fs fCLEARÎ 000, fCLEARÎ 000, g 001, 43 8 g 001, 43 8 fCLEARG 002, 42 34 fCLEARG 002, 42 34 n 003, 11 n 003, 11 z 004, 10 ~ 004, 34 ¼ 005, 12 z 005, 10 Þ 006, 16 ~ 006, 34 P 007, 14 ¼ 007, 12 M 008, 15 Þ 008, 16 P 009, 14 M 010, 15 fs fs REGISTERS n: # Periods. i: Nom.
Section 15: Savings 215 1. Key in the program. 2. RPN: Key in the annual nominal rate as a percentage then press \. 2. ALG: Key in the annual nominal rate as a percentage then press ³. 3. Key in the number of compounding periods per year then press t to obtain the effective annual interest rate. 4. For a new case return to step 2. Example 2: What is the effective annual rate of interest if the annual nominal rate of 5.25% is compounded monthly? Keystrokes (RPN mode) Keystrokes (ALG mode) Display 5.
Section 15: Savings Example: Find the nominal rate compounded quarterly if the effective annual rate is 5.35%. Keystrokes (RPN mode) Keystrokes (ALG mode) f] f[ fCLEARG fCLEARG 4n100$ 4n100$ 100.00 5.35+Þ +5.35³Þ –105.35 M¼ M¼ 1.31 :n§ §:n³ 5.25 Display Percent nominal interest rate. Continuous Rate Converted to Effective Rate This procedure converts a continuous annual interest rate to the effective rate. 1. RPN: Press 1\. 1. ALG: Press 1³. 2.
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 KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY DISPLAY 1 014, 1 z 014, 10 8 015, 8 1 015, 1 0 016, 0 8 016, 8 z 017, 10 0 017, 0 n 018, 11 n 018, 11 gT 019, 24 gT 019, 1 020, 1 1 020, 1 ~ 021, 34 - 021, 30 - 022, 30 ~ 022, 34 :P 023, 14 § 023, 20 § 024, 20 :P 024, ?6 025, 44 6 } 025, :0 026, 45 0 ?6 026, 44 6 gm 027, 43 35 :0 027, 45 0 g(039 028,43, 33, 039 gm 028, 43 35 2 029, 2 g(
Section 16: Bonds KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY 219 DISPLAY :1 039, 45 1 } 039, :6 040, 45 6 g(000 040,43, 33, 000 + 041, 40 :1 041, Þ 042, 16 Þ 042, 16 $ 043, 13 - 043, 30 ¼ 044, 12 :6 044, 2 045, 2 $ 045, 13 § 046, 20 ¼ 046, 12 § 047, 20 2 048, 2 } 049, 36 fs 36 45 1 45 6 fs REGISTERS n: ∆ days/180 i: Yield/2 PV: –Price PMT: Coupon/2. FV: Red+Cpn./2 R0: Yield R1: Price.
Section 16: Bonds 7. If price is desired: a. Key in the desired yield to maturity as a percentage then press ?0. b. Press t to calculate price as a percentage of par value. c. RPN: Press ~ to display accrued interest due the seller. Press + to calculate the total price paid. c. ALG: Press +~ to display accrued interest due the seller and then press } to calculate the total price paid. For a new case return to step 3. Note that only those values which have been changed need to be reentered and stored.
Section 16: Bonds Keystrokes (RPN mode) Keystrokes (ALG mode) Display t t 103.41 Price to yield 4.5% (calculated). ~ +~ 1.33 Accrued interest (calculated). + ³ 104.74 Total price paid. 221 Example 2: The market is quoting 105% for the bond described in example 1. What yield will that provide? What would be the yield to maturity if 104% were the quoted price? Keystrokes (RPN mode) Keystrokes (ALG mode) Display 104.74 From previous example. 0?0 0?0 0.00 105?1t 105?1t 4.
Section 16: Bonds Annual Coupon Bonds For bonds which have annual coupons, use the following hp 12c platinum program to evaluate price and accrued interest on an Actual/Actual day basis. This program may be modified for annual coupon bonds to be calculated on a 30/360 day basis.
Section 16: Bonds KEYSTROKES (RPN mode) KEYSTROKES (ALG mode) DISPLAY gÒ 019, 43 26 ?7 020, 44 :6 021, :4 223 DISPLAY :5 019, 45 5 7 gÒ 020, 43 26 45 6 ?7 021, 44 7 022, 45 4 :6 022, 45 6 gÒ 023, 43 26 :4 023, 45 4 :7 024, 45 7 gÒ 024, 43 26 z 025, 10 z 025, n 026, 11 :7 026, 0 027, 0 n 027, 11 P 028, 14 0 028, 0 M 029, 15 P 029, 14 Þ 030, 16 M 030, 15 :n 031, 45 11 :n 031, :2 032, 45 2 § 032, Þ 033, 16 :2
Section 16: Bonds REGISTERS n: Used i: Yield PV: Used PMT: Cpn. or 0 FV: Used R0: # Periods (n) R1: Yield R2: Coupon R3: Redemption R4: Settlement R5: Next Cpn. R6: Last Coupon R7: Used R8–R.5: Unused For annual coupon bonds calculated on a 30/360 day basis, insert d after gÒ at steps 19 and 23 in the RPN mode program and after gÒ at steps 20 and 24 in the ALG mode (making each program two steps longer). 1. Key in the program and press ?É if the C status indicator is not displayed. 2.
Section 16: Bonds Keystrokes (RPN mode) Keystrokes (ALG mode) Display 100?3 100?3 100.00 Redemption value. 8.152004?4 8.152004?4 8.15 Settlement date. 12.012004?5 12.012004?5 12.01 Next coupon date. t t –4.58 Accrued interest. t t –94.75 Purchase price. File name: hp 12c pt_user's guide_English_HDPMF123E27 Printed Date: 2005/8/1 Page: 225 of 275 Dimension: 14.
Appendices File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 227 of 275 Printed Date: 2005/8/1 Dimension: 14.
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” or collectively as “the stack.”) The stack registers are designated X, Y, Z, and T.
Appendix A: RPN and the Stack 229 Now let’s see what happens in the stack during a chain calculation in RPN mode: (3 × 4) + (5 × 6) 7 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 231 One-Number Functions and the Stack One-number mathematics and number-alteration functions — y, r, °, >, ¡, e, B, Ñ, and T — use only the number in the displayed X-register. When the key is pressed, the function is performed upon the number in the X-register, and the answer is then placed into the X-register. The stack does not lift, so the number formerly in the X-register does not get copied into the Y-register; but this number is copied into the LAST X register.
Appendix A: RPN and the 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. The diagram on the next page illustrates the stack operation when 8 ÷ 2 is calculated.
Appendix A: RPN and the Stack 233 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 Key The number in the displayed X-register is copied into the LAST X register whenever any of the following function keys is pressed: + - § z y q > ¿ r B T Ñ _ ^ Q R e b à Z D Ò ¡ Pressing gF lifts the stack (unless \, O, _ or ^ was the last key pressed, as described on page 230), 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 235 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 — just as you would if you were doing the calculation manually (that is, using pencil and paper).
Appendix A: RPN and the Stack Keystrokes (RPN mode) Display 84000 84,000. Enters base amount into displayed X-register. § 168,000.00 Annual sales after first year. § 336,000.00 Annual sales after second year. § 672,000.00 Annual sales after third year. 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) Although most of this material is included at the appropriate places throughout this manual, it is collected here for easy reference. To select algebraic mode, press f[. When the calculator is in algebraic mode, the ALG status indicator is lit. Note: In ALG mode, it is a good idea to begin calculations by pressing OO. This will ensure that there are no pending arithmetic calculations that might interfere with the solution of a new problem.
Appendix B: Algebraic Mode (ALG) Keystrokes (ALG mode) Display 90.89} –13.54 } completes the calculation. 65gr§12} 96.75 New calculation: z3.5} 27.64 Calculates 96.75 ÷ 3.5 65 × 12 You can also do long calculations without pressing } after each intermediate calculation: just press it at the end. The operators perform from left to right, in the order you enter them. Keying in Negative Numbers ( ) The Þ key changes the sign of a number.
Appendix B: Algebraic Mode (ALG) Keystrokes (ALG mode) Display OO 0.00 456-75z 381.00 18.5§ 20.59 68z 1,400.43 1.9} 737.07 The 239 Clears any pending operations. Key in ALG Mode LAST X in ALG mode is not used in this book. It is the one function that is quite different in ALG and RPN modes. Refer to page 234 for the list of 23 different key presses that cause the displayed X-register to be copied into the LAST X register in RPN mode.
Appendix B: Algebraic Mode (ALG) The stack diagrams showing the output for the Calendar and Financial functions on page 233 are the same for ALG as RPN mode. To add INT and PRICE after executing the bond E function, press +~}. In this case, ~ is used to enter the second argument for the + operation. After executing +~}, the total price (INT + PRICE) will be displayed. LAST X will be unchanged, but the original PRICE will be found in the Y-register.
Appendix B: Algebraic Mode (ALG) 241 Percentage Functions In most cases, b divides a number by 100. The one exception is when a plus or minus sign precedes the number. For instance, 25 b results in 0.25. To find 25% of 200, press: 200 § 25 b}. (Result is 50.) You can also calculate a net amount all in one calculation: For instance, to decrease 200 by 25%, just enter 200-25b}. (Result is 150.) Example: You borrow $1,250 from a relative, and agree to repay the loan in a year with 7% simple interest.
Appendix B: Algebraic Mode (ALG) Percent of Total To calculate what percentage one number is of another: 1. Calculate the total amount by adding all individual amounts. 2. Key in the number whose percentage equivalent you wish to find. 3. Press Z. Example: Last month, your company posted sales of $3.92 million in the U.S., $2.36 million in Europe, and $1.67 million in the rest of the world. What percentage of the total sales occurred in Europe? Keystrokes Display (ALG mode) OO 0.
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 Searching for IRR. You can continue searching for IRR solutions, even after an Error 3 indication, as follows: 1. Make a guess for the interest rate and key it in. 2. Press:gt. Your guess will aid the calculator in its search, and if it finds an IRR answer near your guess, that answer will be displayed.
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 1: Storage Register Overflow Operation ?+(0 through ?-(0 through ?§(0 through ?z(0 through A Condition 4) 4) 4) 4) Magnitude of result is greater than 9.999999999×1099. Error 2: Statistics Operation Condition Ö n (number in R1) = 0 Σx = 0 v n=0 n=1 nΣx2 – (Σx)2< 0 nΣy2 – (Σy)2< 0 R n=0 nΣx2 – (Σx)2 = 0 Q n=0 nΣy2 – (Σy)2 = 0 R~ Q~ [nΣx2 – (Σx)2][nΣy2 – (Σy)2] ≤ 0 Error 3: IRR Refer to Appendix C.
Appendix D: Error Conditions 247 Error 5: Compound Interest Operation Condition n i = 0 and PMT = 0 PMT is between FV × d and –PV × d, inclusive, i ( ) 100 where d = , where S=0 for END S (1 + i × ) 100 mode and 1 for BEG mode. i ≤ –100 ¼ n=0 n ≥ 1010 or n < 0 i ≤ –100 Cash flows all have same sign. $ i ≤ –100 P n=0 i ≤ –100 M i ≤ –100 ! x≤0 x is noninteger.
Appendix D: Error Conditions Error 6: Storage Registers Operation Condition ? Storage register specified does not exist or has been converted to program lines. : K a l L a n specifies a storage register that does not exist or has been converted to program lines. n > 80 n<0 n is noninteger x > 99 x<0 x is noninteger Attempted to input Nj for CF0 Error 7: IRR Refer to Appendix C. File name: hp 12c pt_user's guide_English_HDPMF123E27 Printed Date: 2005/8/1 Page: 248 of 275 Dimension: 14.
Appendix D: Error Conditions 249 Error 8: Calendar Operation Ò Condition D Improper date format or illegal date. D Attempting to add days beyond calculator’s date capacity. E Improper date format or illegal date. S 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).* Error 9: Service Refer to Appendix F. Pr Error z Continuous Memory has been reset.
Appendix E Formulas Used Percentage Base(y ) × Rate(x ) 100 ⎛ NewAmount(x ) − Base(y ) ⎞ ⎟ ∆% = 100⎜⎜ ⎟ Base(y ) ⎠ ⎝ %= ⎛ Amount(x ) ⎞ ⎟ %T = 100⎜⎜ ⎟ ⎝ Total(y ) ⎠ Interest n = number of compounding periods. i = periodic interest rate, expressed as a decimal. PV = present value. FV = future value or balance. PMT S I = periodic payment. = payment mode factor (0 or 1) indicating treatment of PMT. 0 corresponds to End, 1 to Begin. = interest amount. INTG (n) = integer portion of n.
Appendix E: Formulas Used Compound Interest Without an odd period: ⎡1 − (1 + i ) −n ⎤ −n 0 = PV + (1 + iS ) ⋅ PMT ⋅ ⎢ ⎥ + FV (1 + i ) i ⎣⎢ ⎦⎥ With simple interest used for an odd period: ⎡1 − (1 + i ) − INTG(n) ⎤ 0 = PV [1 + iFRAC(n)] + (1 + iS )PMT ⎢ ⎥+ i ⎣⎢ ⎦⎥ FV (1 + i ) −INTG(n) With compound interest used for an odd period: ⎡1 − (1 + i ) − INTG(n) ⎤ 0 = PV (1 + i )FRAC(n) + (1 + iS )PMT ⎢ ⎥+ i ⎣⎢ ⎦⎥ FV (1 + i ) −INTG(n) Amortization n = number of payment periods to be amortized.
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. NPV = CF0 + CF1 1 (1 + i ) + CF2 (1 + i ) 2 + ... + CFn (1 + i )n Internal Rate of Return n = number of cash flows CFj = cash flow at period j.
Appendix E: Formulas Used 253 Bonds Reference: Jan Mayle, TIPS Inc., Standard Securities Calculation Methods, Volume 1, Third Edition, Securities Industry Association Inc., New York, 1993. DIM = days between issue date and maturity date. DSM = days between settlement date and maturity date. DCS = days between beginning of current coupon period and settlement date. E DSC N CPN = number of days in coupon period where settlement occurs.
Appendix E: Formulas Used Black-Scholes Formula for Valuing European Options P = current asset price. r% = risk-free rate (continuous, per time unit). s% = volatility (continuous, per time unit). T = term of option (same time unit as r% and s%). X = exercise price of option. N(z) = probability that a unit normal random variable is less than z.
Appendix E: Formulas Used Straight-Line Depreciation Keyboard function: DPN J = SBV − SAL for j = 1, 2, …, L L Program for partial first year: SBV − SAL Y1 ⋅ L 12 SBV − SAL for j = 2, 3, …, L DPN J = L DPN1 = DPNL + 1 = RDVL Sum-of-the-Years-Digits Depreciation SOYDk = (W + 1)(W + 2F ) 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 DPN j = RBVj −1 ⋅ FACT for j ≠ 1 100L Modified Internal Rate of Return n = number of compounding periods. NFVP = Net future value of the positive cash flows. NPVN = Net present value of the negative cash flows. ⎡ ⎢⎛ NFVP MIRR = 100⎢⎜⎜ − NPVN ⎢⎝ ⎣ 1 ⎤ ⎞n ⎥ ⎟ − 1⎥ ⎟ ⎠ ⎥ ⎦ Advance Payments A PMT = = number of payments made in advance. PV − FV (1 + i ) −n ⎡1 − (1 + i ) −(n − A ) ⎤ + A⎥ ⎢ i ⎣⎢ ⎦⎥ Interest Rate Conversions C = number of compounding periods per year.
Appendix E: Formulas Used Statistics Mean ∑x x= y = n ∑y n Weighted M ean ∑ wx ∑w xw = Linear Estimation n = number of data pairs yˆ = A + Bx xˆ = y−A B where B = ∑x ⋅ ∑y ∑ xy − ∑x 2 n A = y − Bx r= ⎡ ⎢∑ xy − ⎣ ⎡ 2 ⎢∑ x − ⎣⎢ n ( x )2 − ∑ ∑ x ⋅∑ y ⎤ n (∑ x )2 ⎤ ⋅ ⎡ n ⎥ ⎦ 2 ⎥ ⎢∑ y − ⎦⎥ ⎣⎢ (∑ y )2 ⎤ n ⎥ ⎦⎥ Standard Deviation n ∑ x 2 − (∑ x )2 n(n − 1) sx = sy = n ∑ y 2 − (∑ y )2 n(n − 1) Factorial 0! = 1 For n > 1 where n is an integer: n n!= ∏ i i =1 File name: hp 12c pt_user
Appendix E: Formulas Used The Rent or Buy Decision Market Value = PRICE(1 + I)n where: I = appreciation per year (as decimal) n = 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 PV PMT = number of years house is owned = down payment + closing costs = mortgage payment + taxes + maintenance – rent – (% tax) (interest + taxes) FV = net cash proceeds on resale
Appendix F Battery, Warranty, and Service Information Battery The hp 12c platinum is shipped with one 3 Volt CR2032 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 Installing a New Battery The contents of the calculator’s Continuous Memory are preserved for a short time while the battery is out of the calculator (provided that you turn off the calculator before removing the battery). This allows you ample time to replace the battery without losing data or programs. If the battery is left out of the calculator for an extended period, the contents of Continuous Memory may be lost.
Appendix F: Battery, Warranty, and Service Information 261 Verifying Proper Operation (Self-Tests) If it appears that the calculator will not turn on or otherwise is not operating properly, use one of the following procedures. 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. 2. The display will show Pr Error. Pressing any key will clear this message from the display. 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.* 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 263 Warranty hp 12c platinum Financial Calculator; Warranty period: 12 months 1. HP warrants to you, the end-user customer, that HP hardware, accessories and supplies will be free from defects in materials and workmanship after the date of purchase, for the period specified above. If HP receives notice of such defects during the warranty period, HP will, at its option, either repair or replace products which prove to be defective.
Appendix F: 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. Nothing herein should be construed as constituting an additional warranty.
Appendix F: Battery, Warranty, and Service Information Asia Pacific L.America Country : Telephone numbers Australia Singapore +61-3-9841-5211 +61-3-9841-5211 Country : Telephone numbers Argentina Brazil 0-810-555-5520 Sao Paulo 3747-7799; ROTC 0-800-157751 Mx City 5258-9922; ROTC 01-800-472-6684 0800-4746-8368 800-360999 9-800-114726 0-800-10111 1-800-711-2884 Mexico N.
Appendix F: Battery, Warranty, and Service Information installation. In the unlikely event that there is interference to radio or television reception(which can be determined by turning the calculator off and on), the user is encouraged to try to correct the interference by one or more of the following measures: z Reorient or relocate the receiving antenna. z Relocate the calculator, with respect to the receiver. Canada This Class B digital apparatus complies with Canadian ICES-003.
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 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.
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 87). g Shift key. Selects alternate function in blue on the slanted face of the function keys (page 16). fCLEARX after f, g, ?, : or i, cancels that key (page 19). É Enter exponent. After pressing, next numbers keyed in are exponents of 10 (page 18). 0 —9 digits.
Function Key Index Financial CLEAR G Clears contents of financial registers (page 42). × Sets payment mode to Begin for compound interest calculations involving payments (page 46). Â Sets payment mode to End for compound interest calculations involving payments (page 46). Ï Calculates simple interest (page 42). w Stores or computes number of periods in financial problem (page 41). A Multiplies a number in displayed X-register by 12 and stores the resulting value in the n-register (page 49).
Function Key Index Ö Computes mean Modes (average) of x-values and ] sets calculator to y-values using RPN mode (page 19). accumulated statistics (page 94). [ sets calculator to algebraic (ALG) mode Computes weighted (page 19). average of y-(item) and x-(weight) values using accumulated statistics (page 99). v Computes sample standard deviations of xand y-values using accumulated statistics (page 96). R 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: Run Mode Pressed from keyboard: t Run/Stop. Begins execution of a stored program. Stops execution if program is running (page 106). 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 114) i Go to. Followed by a three-digit number, positions calculator to that line in program memory. No instructions are executed (page 125). Ç Single step.
Subject Index Bonds, 82–83, 217–25, 253, 268 Bonds, 30/360 day basis, 217–21 Bonds, annual coupon, 222 Bonds, corporate, 82 Bonds, municipal, 82 Bonds, U.S.
Subject Index Compound interest, 49–68, 251 Compound interest calculation, 12 Compounding periods, 44, 49 Conditional branching, 129–30 Conditional test instructions, 129 Constants, arithmetic calculations with, 235 Constants, arithmetic calculations with, 91 Continuous compounding, 216, 256 Continuous memory, 86 Continuous memory, resetting of, 42, 47, 86, 88, 112 Continuous rate, 216 D , 37–40 , 84, 230 , 65, 230 , 38 D.
Subject Index 143, 230 , 114, 139 000, 112–13 I , 13, 41, 42 , 42, 230 , 13, 72, 73, 78, 243 , 101, 231 Indicators, status, 87 Instructions in program lines, 108 Interest rate, annual, 55 Interest rate, periodic, 55 Interest, simple, 42 Internal rate of return, 72 Internal rate of return, calculating, 78 Internal rate of return, modified, 192 Interrupting a program, 117 IRR, 72, 192 K Keyboard, 16 L , 91, 101, 234 , 100, 231 LAST X register, 86 Leasing, 202 Linear estimation, 97 Logarithm, 100 Loopi
Subject Index , 41, 42, 55 Parentheses Calculations, 26, 240 Partial-year depreciation, 171 Payment, 45, 209 Payment amount, calculating, 59 Payment mode, 46 Payments, advance, 202, 209 Payments, number of, 49 Percent difference, 34, 241 Percent of total, 35, 242 Percentages, 31, 32, 241 PMT, 45 Populations, 96 Power function, 102, 242 Pr error, 90 Prefix key, 16 Present value, 45 Present value, calculating, 56 PRGM status indicator, 104, 106 Program branching, 125 Program editing, 139 Program lines, displ
Subject Index X Y , 40, 42, 69, 82, 90, 94, 96, 125, 129, 230 , 100, 231 , 94, 230 , 97, 230 , 99, 125, 129 File name: hp 12c pt_user's guide_English_HDPMF123E27 Printed Date: 2005/8/1 , 13, 82, 83 , 97, 230 , 102, 231 , 230 Yield, 206, 212 Page: 278 of 275 Dimension: 14.
