hp 12c financial calculator user's guide H Edition 4 HP Part Number 0012C-90001 File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 1 of 209 Printed Date: 2005/7/29 Dimension: 14.
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Introduction About This Handbook This hp 12c user's guide is intended to help you get the most out of your investment in your hp 12c Programmable Financial Calculator. Although the excitement of acquiring this powerful financial tool may prompt you to set this handbook aside and immediately begin “pressing buttons,” 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.
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 Clearing the Financial Registers .............................................. 33 Simple Interest Calculations........................................................... 33 Financial Calculations and the Cash Flow Diagram.......................... 34 The Cash Flow Sign Convention.............................................. 36 The Payment Mode ............................................................... 37 Generalized Cash Flow Diagrams ...........................................
Contents 7 Section 6: Statistics Functions ........................................ 76 Accumulating Statistics .................................................................. 76 Correcting Accumulated Statistics ...................................................77 Mean .........................................................................................77 Standard Deviation.......................................................................79 Linear Estimation ..................................
Contents Section 11: Multiple Programs ...................................... 120 Storing Another Program ............................................................ 120 Running Another Program........................................................... 122 Part III. Solutions .................................................. 123 Section 12: Real Estate and Lending .............................. 124 Annual Percentage Rate Calculations With Fees.............................
Contents 9 Appendixes ................................................................ 169 Appendix A: The Automatic Memory Stack ................... 170 Getting Numbers Into the Stack: The Key..............................171 Termination of Digit Entry .....................................................172 Stack Lift.............................................................................172 Rearranging Numbers in the Stack ...............................................172 The key ................
Contents 30/360 Day Basis.............................................................. 187 Bonds ...................................................................................... 188 Depreciation ............................................................................. 189 Straight-Line Depreciation..................................................... 189 Sum-of-the-Years-Digits Depreciation ...................................... 189 Declining-Balance Depreciation ............................
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. While working through the examples below, don’t be concerned about learning how to use the calculator; we’ll cover that thoroughly beginning with Section 1. Example 1: Suppose you want to ensure that you can finance your daughter’s college education 14 years from today. You expect that the cost will be about $6,000 a year ($500 a month) for 4 years.
Making Financial Calculations Easy Note: A battery symbol (¼) shown in the lower-left corner of the display when the calculator is on signifies that the available battery power is nearly exhausted. To install new batteries, refer to Appendix E. The calendar functions and nearly all of the financial functions take some time to produce an answer. (This is typically just a few seconds, but the ¼, !, L, and S functions could require a half-minute or more.
Making Financial Calculations Easy 13 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 – 10,470.85 = 10,925.76). Suppose you make monthly payments, beginning at the end of next month, into an account that pays 6% annually, compounded monthly. What payment amount would be required in order to accumulate $10,925.
Part I Problem Solving File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 15 of 209 Printered Date: 2005/7/29 Dimension: 14.
Section 1 Getting Started Power On and Off To begin using your hp 12c, press the ; key*. Pressing ; again turns the calculator off. If not manually turned off, the calculator will turn off automatically 8 to 17 minutes after it was last used. Low-Power Indication A battery symbol (¼) 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 E.
Section 1: Getting Started 17 Throughout this handbook, references to the operation of an alternate function appear as only the function name in a box (for example, “The L function …”). References to the selection of an alternate function appear preceded by the appropriate prefix key (for example, “Pressing fL …”).
Section 1: Getting Started Keying in Large Numbers Since the display cannot show more than 10 digits of a number, numbers greater than 9,999,999,999 cannot be entered into the display by keying in all the digits in the number. However, such numbers can be easily entered into the display if the number is expressed in a mathematical shorthand called “scientific notation.” To convert a number into scientific notation, move the decimal point until there is only one digit (a nonzero digit) to its left.
Section 1: Getting Started 19 Simple Arithmetic Calculations Any simple arithmetic calculation involves two numbers and an operation — addition, subtraction, multiplication, or division. To do such a calculation on your hp 12c, you first tell the calculator the two numbers, then tell the calculator the operation to be performed. The answer is calculated when the operation key (+,-,§, or z) is pressed.
Section 1: Getting Started Chain Calculations 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 21 Keystrokes 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 Your hp 12c calculates the answer in just the same way: Keystrokes 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 23 Storage Registers Numbers (data) in the hp 12c are stored in memories called “storage registers” or simply “registers.” (The singular term “ memory” is sometimes used in this handbook to refer to the entire collection of storage registers.
Section 1: Getting Started Later that same day … Keystrokes Display ; 2,500.00 Turns the calculator back on. :1 3,250.00 Recalls the cost of the computer to the display. 6§ 19,500.00 Multiplies the quantity ordered to get :2 2,500.00 + 22,000.00 Total invoice. the cost of the computers. Recalls the cost of the printer to the display. Clearing Storage Registers To clear a single storage register — that is, to replace the number in it with zero — merely store zero into it.
Section 1: Getting Started 25 Storage register arithmetic is possible with only registers R0 through R4. Example: In the example on page 20, we updated the balance in your checkbook. Let’s suppose that because data is stored indefinitely in your calculator’s Continuous Memory, you keep track of your checking account balance in the calculator. You could use storage register arithmetic to quickly update the balance after depositing or writing checks. Keystrokes Display 58.33?0 58.
Section 2 Percentage and Calendar Functions Percentage Functions The hp 12c includes three keys for solving percentage problems: b, à, and Z. You don’t need to convert percentages to their decimal equivalents; this is done automatically when you press any of these keys. Thus, 4% need not be changed to 0.04; you key it in the way you see and say it: 4b. Percentages 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.
Section 2: Percentage and Calendar Functions 27 Net Amount A net amount — that is, the base amount plus or minus the percentage amount — can be calculated easily with your hp 12c, since the calculator holds the base amount inside after you calculate a percentage amount. To calculate a net amount, simply calculate the percentage amount, then press = or -. Example: You’re buying a new car that lists for $13,250. The dealer offers you a discount of 8%, and the sales tax is 6%.
Section 2: Percentage and Calendar Functions The à key can be used for calculations of the percent difference between a wholesale cost and a retail cost. If the base number entered is the wholesale cost, the percent difference is called the markup; if the base number entered is the retail cost, the percent difference is called the margin. Examples of markup and margin calculations are included in the hp 12c Solutions Handbook. Percent of Total To calculate what percentage one number is of another: 1.
Section 2: Percentage and Calendar Functions 29 To find what percentage a number is of a total, when you already know the total number: 1. Key in the total number. 2. Press \ to separate the other number from the total number. 3. Key in the number whose percentage equivalent you wish to find. 4. Press Z. For example, if you already knew in the preceding example that the total sales were $7.95 million and you wanted to find what percentage of that total occurred in Europe: Keystrokes Display 7.95\ 7.
Section 2: Percentage and Calendar Functions Day-Month-Year. To set the date format to day-month-year, press gÔ. To key in a date with this format in effect: 1. Key in the one or two digits of the day. 2. Press the decimal point key (.). 3. Key in the two digits of the month. 4. Key in the four digits of the year. For example, to key in 7 April, 2004: Keystrokes Display 7.042004 7.042004 When the date format is set to day-month-year, the D.MY status indicator in the display is lit. If D.
Section 2: Percentage and Calendar Functions 31 Keystrokes Display 14.052004\ 14.05 120gD 11,09,2004 6 The expiration date is 11 September Keys in date and separates it from number of days to be entered. 2004, a Saturday. When D is executed as an instruction in a running program, the calculator pauses for about 1 second to display the result, then resumes program execution. Number of Days Between Dates To calculate the number of days between two given dates: 1. Key in the earlier date and press \.
Section 3 Basic Financial Functions The Financial Registers In addition to the data storage registers discussed on page 23, the hp 12c has five special registers in which numbers are stored for financial calculations. These registers are designated n, i, PV, PMT, and FV.
Section 3: Basic Financial Functions 33 Clearing the Financial Registers Every financial function uses numbers stored in several of the financial registers. Before beginning a new financial calculation, it is good practice to clear all of the financial registers by pressing fCLEARG. Frequently, however, you may want to repeat a calculation after changing a number in only one of the financial registers. To do so, do not press fCLEARG; instead, simply store the new number in the register.
Section 3: Basic Financial Functions Keystrokes Display 7¼ 7.00 Stores the annual interest rate. 450Þ$ –450.00 Stores the principal. fÏ 5.25 Accrued interest, 360-day basis. + 455.25 Total amount: principal plus accrued interest. Example 2: Your friend agrees to the 7% interest on the loan from the preceding example, but asks that you compute it on a 365-day basis rather than a 360-day basis.
Section 3: Basic Financial Functions 35 The exchange of money in a problem is depicted by vertical arrows. Money you receive is represented by an arrow pointing up from the point in the time line when the transaction occurs; money you pay out is represented by an arrow pointing down. Suppose you deposited (paid out) $1,000 into an account that pays 6% annual interest and is compounded monthly, and you subsequently deposited an additional $50 at the end of each month for the next 2 years.
Section 3: Basic Financial Functions The form in which n is entered determines whether or not the calculator performs financial calculations in Odd-Period mode (as described on pages 50 through 53). If n is a noninteger (that is, there is at least one nonzero digit to the right of the decimal point), calculations of i, PV, PMT, and FV are performed in Odd-Period mode. z i is the interest rate per compounding period.
Section 3: Basic Financial Functions 37 The Payment Mode One more bit of information must be specified before you can solve a problem involving periodic payments. Such payments can be made either at the beginning of a compounding period (payments in advance, or annuities due) or at the end of the period (payments in arrears, or ordinary annuities). Calculations involving payments in advance yield different results than calculations involving payments in arrears.
Section 3: Basic Financial Functions File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 38 of 209 Printered Date: 2005/7/29 Dimension: 14.
Section 3: Basic Financial Functions 39 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 Keystrokes Display 12z 27.33 41 Twenty-seven years and four months. Because the calculator rounds the calculated value of n up to the next higher integer, in the preceding example it is likely that — while 328 payments will be required to pay off the loan — only 327 full payments of $325 will be required, the next and final payment being less than $325. You can calculate the final, fractional, 328th payment as follows: Keystrokes Display 328n 328.
Section 3: Basic Financial Functions Example 2: You’re opening a savings account today (the middle of the month) with a $775 deposit. The account pays 61/4% interest compounded semimonthly. If you make semimonthly deposits of $50 beginning next month, how long will it take for your account to reach $4000? Keystrokes Display fCLEARG 6.25\24z¼ 0.26 Calculates and stores i. 775Þ$ –775.00 Stores PV (with minus sign for cash paid out). 50ÞP –50.00 Stores PMT (with minus sign for cash paid out).
Section 3: Basic Financial Functions 43 Keystrokes Display MM 4,027.27 Calculates FV – which equals the balance in the account if 58 full deposits were made.* :P –50.00 Recalls amount of deposits. + 3,977.27 Calculates the balance in the account if 57 full deposits were made and interest accrued during the 58th month.† 4000- –22.73 Calculates final, fractional, 58th deposit required to reach $4,000. Calculating the Periodic and Annual Interest Rates 1.
Section 3: Basic Financial Functions Example: What annual interest rate must be obtained to accumulate $10,000 in 8 years on an investment of $6,000 with quarterly compounding? Keystrokes Display fCLEARG 8\4§w 32.00 6000Þ$ –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 45 Example 1: You’re financing a new car purchase with a loan from an institution that requires 15% interest compounded monthly over the 4-year term of the loan. If you can make payments of $150 at the end of each month and your down payment will be $1,500, what is the maximum price you can pay for the car? (Assume the purchase date is one month prior to the date of the first payment.) Keystrokes Display fCLEARG 4gA 48.00 Calculates and stores n. 15gC 1.
Section 3: Basic Financial Functions Keystrokes Display fCLEARG 5n 5.00 Stores n. 12¼ 12.00 Stores i. 17500P 17,500.00 Stores PMT. Unlike in the previous problem, here PMT is positive since it represents cash received. 540000M 540,000.00 Stores FV. g 540,000.00 Sets payment mode to End. $ –369,494.09 The maximum purchase price to provide a 12% annual yield. PV is displayed with a minus sign since it represents cash paid out. Calculating the Payment Amount 1.
Section 3: Basic Financial Functions 47 Keystrokes Display fCLEARG 29gA 348.00 Calculates and stores n. 14.25gC 1.19 Calculates and stores i. 43400$ 43,400.00 Stores PV. g 43,400.00 Sets payment mode to End. P –523.99 Monthly payment (with minus sign for cash paid out). Example 2: Looking forward to retirement, you wish to accumulate $60,000 after 15 years by making deposits in an account that pays 93/4% interest compounded semiannually.
Section 3: Basic Financial Functions Calculating the Future Value 1. Press fCLEARG to clear the financial registers. 2. Enter the number of payments or periods, using n or A. 3. Enter the periodic interest rate, using ¼ or C. 4. Enter either or both of the following: z Present value, using $. z Payment amount, using P. Note: Remember to observe the cash flow sign convention. 5. If a PMT was entered, press g× or g to set the payment mode. 6. Press M to calculate the future value.
Section 3: Basic Financial Functions 49 Example 2: If you deposit $50 a month (at the beginning of each month) into a new account that pays 61/4% annual interest compounded monthly, how much will you have in the account after 2 years? 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.
Section 3: Basic Financial Functions Keystrokes Display 2Þ¼ –2.00 Stores i (with minus sign for a “negative interest rate”). 32000Þ $ –32,000.00 Stores PV (with minus sign for cash paid out). M 28,346.96 Property value after 6 years. 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.
Section 3: Basic Financial Functions 51 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 Example 1: A 36-month loan for $4,500 accrues interest at a 15% annual percentage rate (APR), with the payments made at the end of each month. If interest begins accruing on this loan on February 15, 2004 (so that the first period begins on March 1, 2004), calculate the monthly payment, with the odd days counted on the basis of a 30-day month and compound interest used for the odd period. Keystrokes Display fCLEARG Clears financial registers.
Section 3: Basic Financial Functions 53 Example 2: A 42-month car loan for $3,950 began accruing interest on July 19, 2004, so that the first period began on August 1, 2004. Payments of $120 are made at the end of each month. Calculate the annual percentage rate (APR), using the actual number of odd days and simple interest for the odd period. Keystrokes Display fCLEARG Clears financial registers. ?Æ Turns off the C indicator in the display, so that simple interest will be used for the odd period.
Section 3: Basic Financial Functions Amortization The hp 12c 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 C. 3. Enter the amount of the loan (the principal), using $. 4.
Section 3: Basic Financial Functions 55 Keystrokes Display 573.35ÞP –573.35 Enters PMT (with minus sign for cash paid out). g –573.35 Sets payment mode to End. 12f! –6,608.89 Portion of first year’s payments (12 ~ –271.31 :$ 49,728.69 Balance remaining after 1 year. :n 12.00 months) applied to interest. Portion of first year’s payments applied to principal. Total number of payments amortized.
Section 3: Basic Financial Functions Keystrokes Display 1f! –552.08 Portion of first payment applied to interest. ~ –21.27 Portion of first payment applied to principal. 1f! –551.85 Portion of second payment applied to interest. ~ –21.50 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 46. 2.
Section 4 Additional Financial Functions Discounted Cash Flow Analysis: NPV and IRR The hp 12c provides functions for the two most widely-used methods of discounted cash flow analysis: l (net present value) and L (internal rate of return). These functions enable you to analyze financial problems involving cash flows (money paid out or received) occurring at regular intervals.
Section 4: Additional Financial Functions z If NPV is positive, the financial value of the investor’s assets would be increased: the investment is financially attractive. z If NPV is zero, the financial value of the investor’s assets would not change: the investor is indifferent toward the investment. z 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 59 The amounts of the subsequent cash flows are stored – in the order they occur – in the remaining storage registers: CF1 thru CF9 in R1 thru R9, and CF10 thru CF19 in R.0 thru R.9, respectively. If there is a CF20, that amount is stored in the FV register.* Each cash flow (CF1, CF2, etc.) is designated CFj, where j takes on values from 1 up to the number of the final cash flow. The amount of a cash flow is entered using the K key.
Section 4: Additional Financial Functions Example: An investor has an opportunity to buy a duplex for $80,000 and would like a return of at least 13%. He expects to keep the duplex 5 years and then sell it for $130,000; and he anticipates the cash flows shown in the diagram below. Calculate NPV to determine whether the investment would result in a return or a loss. Note that although a cash flow amount ($4,500) occurs twice, these cash flows are not consecutive.
Section 4: Additional Financial Functions 61 Calculating NPV for Grouped Cash Flows. A maximum of 20 cash flow amounts (in addition to the initial investment CF0) can be stored in the hp 12c.* However, problems involving more than 20 cash flows can be handled if among the cash flows there are equal consecutive cash flows. For such problems, you merely enter along with the amounts of the cash flows the number of times — up to 99 — each amount occurs consecutively.
Section 4: Additional Financial Functions Example: An investor has an opportunity to purchase a piece of property for $79,000; and he would like a 131/2% return.
Section 4: Additional Financial Functions 63 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 L function may take a significant amount of time to produce an answer, during which the calculator displays running.
Section 4: Additional Financial Functions The complex mathematical characteristics of the IRR computation have an additional ramification: Depending on the magnitudes and signs of the cash flows, the computation of IRR may have a single answer, multiple answers, a negative answer or no answer.* For additional information regarding L, refer to Appendix B. For an alternative method of calculating IRR, refer to Section 13.
Section 4: Additional Financial Functions 65 Keystrokes Display :ga 2.00 N5 7n 7.00 Resets the number in the n register to its original value. To display all the cash flow amounts and the number of times they occur consecutively: Keystrokes Display :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.
Section 4: Additional Financial Functions 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 $9,000, then calculate the new NPV for a 131/2% return.
Section 4: Additional Financial Functions 67 To calculate bond price and yield for a 30/360 bond (that is, using the basis of a 30day month and a 360-day year — such as for municipal bonds, corporate bonds, and state and local government bonds), and to calculate bond price for bonds with an annual coupon payment, refer to Section 16: Bonds. Bond Price 1. Enter the desired yield to maturity (as a percentage), using ¼. 2. Enter the annual coupon rate (as a percentage), using P. 3.
Section 4: Additional Financial Functions Example: The market is quoting 883/8% for the bond described in the preceding example. What yield will that provide? Keystrokes Display 3\8z 0.38 Calculates 3/8. 88+$ 88.38 Enters quoted price. 6.75P 6.75 Enters coupon rate. 4.282004\ 4.28 Enters settlement (purchase) date. 6.042018 6.042018 Enters maturity (redemption) date. fS 8.15 Bond yield.
Section 4: Additional Financial Functions 69 Example: A metalworking machine, purchased for $10,000, is depreciated over 5 years. Its salvage value is estimated at $500. Find the depreciation and remaining depreciable value for the first 3 years of the machine’s life using the declining-balance method at double the straight-line rate (200 percent declining-balance). Keystrokes Display 10000$ 10,000.00 Enters original cost. 500M 500.00 Enters salvage value. 5n 5.00 Enters expected useful life.
Section 5 Additional Operating Features Continuous Memory The calculator’s Continuous Memory contains the data storage registers, the financial registers, the stack and LAST X registers, program memory, and status information such as display format, date format, and payment mode. All information in Continuous Memory is preserved even while the calculator is turned off.
Section 5: Additional Operating Features 71 The Display Status Indicators Six 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. Keystrokes Display 19.
Section 5: Additional Operating Features Keystrokes Display f4 14.8746 f1 14.9 f0 15. f9 14.87456320 Although nine decimal places were specified after f, only eight are displayed since the display can show a total of only 10 digits. The standard display format, plus the specified number of decimal places, remain in effect until you change them; they are not reset each time the calculator is turned on.
Section 5: Additional Operating Features Keystrokes Display f. 1.487456 01 73 The exponent in this example indicates that the decimal point should be moved one decimal place to the right, giving the number 14.87456, which is the first seven digits of the number previously in the display. To set the display back to standard display format, press f followed by the desired number of decimal places.
Section 5: Additional Operating Features Errors. If you attempt an improper operation — such as division by zero — the calculator will display the word Error followed by a digit (0 through 9). To clear the Error display, press any key. This does not execute that key’s function, but does restore the calculator to its condition before the improper operation was attempted. Refer to Appendix C for a list of error conditions. Pr Error.
Section 5: Additional Operating Features 75 Arithmetic Calculations With Constants Example: At Permex Pipes a certain pipe fitting is packaged in quantities of 15, 75, and 250. If the cost per fitting is $4.38, calculate the cost of each package. Keystrokes Display 15\ 15.00 Keys first quantity into calculator. 4.38 4.38 Keys unit cost into display. § 65.70 Cost of a package of 15. 75 75. Keys second quantity into display. gF 4.
Section 6 Statistics Functions Accumulating Statistics The hp 12c can perform one- or two-variable statistical calculations. The data is entered into the calculator using the _ key, which automatically calculates and stores statistics of the data into storage registers 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 77 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 Hours/Week 1 32 $17,000 2 40 $25,000 3 45 $26,000 4 40 $20,000 5 38 $21,000 6 50 $28,000 7 35 $15,000 To find the average workweek and sales of this sample: Keystrokes Display fCLEAR² 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 79 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 v is pressed; to display the standard deviation of the y-values, press ~.
Section 6: Statistics Functions Linear Estimation With two-variable statistical data accumulated in the statistics registers, you can estimate a new y-value ( ŷ ) given a new x-value, and estimate a new x-value ( x̂ ) given a new y-value. To calculate ŷ : 1. Key in a new x-value. 2. Press gR. To calculate x̂ : 1. Key in a new y-value. 2. Press gQ.
Section 6: Statistics Functions 81 Example: Compute the slope and intercept of the regression line in the preceding example. Keystrokes Display 0gR 15.55 y-intercept (A); projected value for x = 0. 1 gR~d~- 0.001 Slope of the line (B); indicates the change in the projected values caused by an incremental change in the x value. The equation that describes the regression line is: y = 15.55 + 0.
Section 6: Statistics Functions Keystrokes Display g 1.19 Weighted mean cost per gallon. A procedure for calculating the standard deviation and standard error (as well as the mean) of weighted or grouped data is included in the hp 12c Solutions Handbook. File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 82 of 209 Printered Date: 2005/7/29 Dimension: 14.
Section 7 Mathematics and Number-Alteration Functions The hp 12c provides several keys for mathematical functions and for altering, numbers. These functions are useful for specialized financial calculations as well as for general mathematics calculations. One-Number Functions Most of the mathematics functions require that only one number be in the calculator (that is, the number in the display) before the function key is pressed.
Section 7: Mathematics and Number-Alteration Functions Fractional. Pressing gT replaces the number in the display by its fractional portion — that is, it replaces all digits to the left of the decimal point by 0. Like Ñ, T changes the number inside the calculator as well as its displayed version. The original number can be recalled to the display by pressing gF. All of the above functions are used basically in the same way. For example, to find the reciprocal of 0.258: Keystrokes Display .258 0.
Section 7: Mathematics and Number-Alteration Functions 85 The Power Function Pressing q calculates a power of a number — that is, yx. Like the arithmetic function +, q requires two numbers: 1. Key in the base number (which is designated by the y on the key). 2. Press \ to separate the second number (the exponent) from the first (the base). 3. Key in the exponent (which is designated by the x on the key). 4. Press q to calculate the power. To Calculate Keystrokes Display 21.4 2\1.4q 2.64 2–1.4 2\1.
Part II Programming File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 87 of 209 Printered Date: 2005/7/29 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 Keystrokes Display - 150.00 Price less discount. 5 5. Handling charge. + 155.00 Net cost (price less discount plus handling charge). 89 Next, set the calculator to Program mode and erase any program(s) already stored: Keystrokes Display fs 00- Sets calculator to Program mode. fCLEARÎ 00- Clears program(s). Finally, press the keys that we used above to solve the problem manually. Do not key in 200; this number will vary each time the program is used.
Section 8: Programming Basics Example: Run the program created above to calculate the net cost of a typewriter listing for $625 and an executive chair listing for $159. Keystrokes Display fs 155.00 Sets calculator to Run mode. Display shows number previously calculated. 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.
Section 8: Programming Basics 91 Identifying Instructions in Program Lines Each key on the hp 12c keyboard — except for the digit keys 0 through 9 — is identified by a two-digit “keycode” that corresponds to the key’s position on the keyboard.
Section 8: Programming Basics Displaying Program Lines Pressing fs to set the calculator from Run mode to Program mode displays the line number and keycode for the program line to which the calculator is currently set. Occasionally you’ll want to check several or all of the instructions stored in program memory.
Section 8: Programming Basics 93 Program line 07 contains the last instruction you keyed into program memory. However, if you press Ê again, you’ll see that this is not the last line stored in program memory: Keystrokes Display Ê 08- 43, 33 00 Program line 08 As you should now be able to tell from the keycodes displayed, the instruction in program line 08 is gi00.
Section 8: Programming Basics Expanding Program M emory If no instructions have been keyed into program memory, if Continuous Memory has been reset, or if fCLEARÎ has been pressed (in Program mode), program memory consists of 8 program lines, and there are 20 storage registers available for storage of data. As you key in a ninth instruction, storage register R.9 is automatically converted into seven new lines of program memory.
Section 8: Programming Basics 95 Program memory is automatically expanded like this whenever another seven instructions have been keyed into program memory — that is, when you key an instruction into program line 16, 23, 30 etc. In each case, the additional program lines made available are converted, seven lines at a time, from the last available data storage register (whether or not data has been stored in that register; if it has, it will be lost).
z Section 8: Programming Basics With the calculator in Run mode, pressing gi followed by two digit keys sets the calculator to the program line specified by the digit keys. Since the calculator is not in Program mode, the line number and keycode are not displayed. The decimal point is not necessary if the calculator is in Run mode, but it is necessary if the calculator is in Program mode.
Section 8: Programming Basics Keystrokes Display 2. Ç Result of executing program line 02. 03- 5 Program line 03: 5. 25. Ç Result of executing program line 03. 04- 25 Program line 04: b 156.25 Ç Result of executing program line 04. 05- 30 Program line 05: - 468.75 Ç Result of executing program line 05. 06- 5 Program line 06: 5 5. Ç 97 Result of executing program line 06. 07- 40 Program line 07: + 473.75 Result of executing program line 07 (the last line of the program).
Section 8: Programming Basics Example: Create a program that calculates the entries in the AMOUNT, TAX, and TOTAL columns for each item on the jewelry distributor’s invoice shown on the next page, and also calculates the total in each of these columns for all items on the invoice. Assume the sales tax is 63/4%. To conserve lines of program memory, instead of keying in the tax rate before the b instruction we’ll store it in register R0 and recall it before the b instruction.
Section 8: Programming Basics 99 Pressing the gu keys is not necessary when we do the calculations manually, since in Run mode the result of every intermediate calculation is displayed automatically; but we’ll include u instructions in the program so that the intermediate results AMOUNT and TAX are automatically displayed when the program is executed. Keystrokes Display 6.75?0 6.75 Stores tax rate in R0. fCLEAR² 0.00 Clears the registers in R1 through R6. 13 13. Keys in quantity of item. \ 13.
Section 8: Programming Basics Keystrokes Display gu 06- ?+2 07- 44 40 + 08- ?+3 09- 44 40 43 31 Pauses to display TAX. 2 40 3 Now, to run the program: Keystrokes Display fs 950.61 Sets calculator to Run mode. fCLEAR² 0.00 Clears registers R1– R6. Stores tax rate. 6.75?0 13\68.5 68.5 Enters quantity and price of first item on invoice. t 890.50 AMOUNT for first item. 60.11 TAX for first item. 950.61 TOTAL for first item. 18\72.9 72.
Section 8: Programming Basics 101 If the duration of the pause is not long enough to write down the number displayed, you can prolong it by using more than one u instruction. Alternatively, you can have the program automatically stop as described next. Stopping Program Execution Stopping Program Execution Automatically. Program execution is automatically halted when the program executes a t instruction. To resume executing the program from the program line at which execution was halted, press t.
Section 8: Programming Basics Keystrokes Display 24\85 85. Third item. t 2,040.00 AMOUNT for third item. 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 :0 02- 45 105 0 Recalls the number of payments to be amortized. This program line is the one to which program execution will later branch. It is included because after the first time the loop is executed, the number in the “display”* is replaced by the result of !. f! 03- 42 11 Amortizes payment(s). gu 04- 43 31 Pauses to display amount of ~ 05- payment(s) applied to interest.
Section 9: Branching and Looping Keystrokes Display Ê 02- 45 0 Line 02: :0. This is the beginning of the first pass through the loop. 1.00 Ê 03- 42 11 Line 03: f!. –531.25 Ê 04- Portion of first month’s payment applied to interest. 43 31 Line 04: gu. –531.25 Ê 05- 34 Line 05: ~. –12.10 Ê 06- Portion of first month’s payment applied to principal. 43 31 Line 06: gu. –12.10 Ê 07- 43, 33 02 Line 07: gi02. This is the end of the first pass through the loop. –12.
Section 9: Branching and Looping Keystrokes Display Ê 07- 43, 33 107 02 Line 07: gi02. This is the end of the second pass through the loop. –12.23 t t(or any key) –530.99 Portion of third month’s payment applied to interest. –12.36 Portion of third month’s payment applied to principal. –12.36 Halts program execution. 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 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 109 We’ll key the income into the display before running the program so that it will be in the X-register when the :0 instruction in program line 01 is executed. This instruction will place the test value 20,000 in the X-register and (as explained in Appendix A) move the income into the Y-register.
Section 9: Branching and Looping Keystrokes Display gi07 04- 43, 33 07 If condition is true, branches to program line 07. :2 05- 45 gi08 06- 43, 33 :1 07- b 08- fs –12.36 2 If condition is false, recalls 25% tax rate to X-register. 08 Branches to program line 08. 45 1 Recalls 20% tax rate to X-register. 25 Calculates tax. Sets calculator to Run mode. (Display shows results of running of previous program.
Section 9: Branching and Looping Keystrokes 111 Display 15,000.00 Ê 07- 45 20.00 Ê 1 Line 07: :1. 20% tax rate has been recalled to X-register, moving income to Y-register. 08- 25 Line 08: b. 3,000.00 20% of 15,000 = 3,000. 20000 20,000. Keys income equal to test value into display and X-register. Ê 01- 45 20,000.00 Ê 02- 03- Test value has been recalled to X-register, moving income to Y-register. 34 Line 02: ~. 20,000.00 Ê 0 Line 01: :0.
Section 9: Branching and Looping Keystrokes Display Ê 02- 34 Line 02: ~. 25,000.00 Ê 03- 43 Income has been placed in X-register and test value has been placed in Y-register. 34 Line 03: go. 25,000.00 Ê 05- 45 2 Condition tested by o was false, so program execution skipped the next line and continued at line 05: :2. 25.00 Ê 06- 43, 33 25% tax rate has been recalled to X-register, moving income to Y-register. 08 Line 06: gi08. 25.00 Ê 08- 25 Line 08: b. 6,250.
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 Display 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. Adding Instructions at the End of a Program To add one or more instructions at the end of the last program stored in program memory: 1. Press fs to set the calculator to Program mode. 2. Press gi.
Section 10: Program Editing 115 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 Example: Assuming you have added a - instruction at the end of program memory as in the preceding example, suppose you now wanted to insert an t instruction before the - instruction so that the program will display the amount of the tax before displaying the net income after tax.
Section 10: Program Editing 117 5. Press gi00. This automatically converts a data storage register into seven additional lines of program memory (if there was not already a i00 instruction remaining at the end of program memory), and it ensures that program execution will branch to line 00 after the program is run. 6. Key in the instruction(s) being added. 7.
Section 10: Program Editing Keystrokes Display :3 12- ~ 13- go 14- 43 34 gi00 15- 43, 33 00 :0 16- 45 0 Keys in instruction immediately following point at which new instructions are being added. (This instruction was replaced in line 01 by i12 instruction.) gi02 17- 43, 33 02 Branches back to second line (line 02) following point at which new instructions are being added. fs 12,000.00 Sets calculator back to Run mode. 7500?3 7,500.00 Stores test value in register R3.
Section 10: Program Editing File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 119 of 209 Printered Date: 2005/7/29 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 121 Example 1: Assuming that program memory still contains the last program from the preceding section (which consisted of 17 program lines), store after that program the office-supplies program from Section 8 (page 88). Since this is the second program to be stored in program memory, we’ll ensure that a i00 instruction separates it from the first program by doing step 3 in the procedure above.
Section 11: Multiple Programs Example 2: With the two programs now stored in program memory from the preceding examples (occupying 27 program lines), store the amortization program from Section 9(page 103). Since there are already two programs stored in program memory, we’ll skip step 3 in the procedure above. Furthermore, since the amortization program ends with a loop, we’ll skip steps 5 and 6.
Part III Solutions File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 123 of 209 Printered Date: 2005/7/29 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 125 Example 1: A borrower is charged 2 points for the issuance of his mortgage. If the mortgage amount is $60,000 for 30 years and the interest rate is 111/2% per year, with monthly payments, what true annual percentage rate is the borrower paying? (One point is equal to 1% of the mortgage amount.) Keystrokes Display g fCLEARG 30gA 360.00 Months (into n) 11.5gC 0.96 Percent monthly interest rate (into i). 60000$ 60,000.00 Loan amount (into PV). P –594.
Section 12: Real Estate and Lending Example 3: Again using the information given in example 1, what is the APR if the mortgage fee is stated as 2 points plus $150? Keystrokes Display g fCLEARG 30gA 360.00 Months (into n) 11.5gC 0.96 Percent monthly interest rate (into i). 60000$ 60,000.00 Loan amount (into PV). P –594.17 Monthly payment (calculated). :$2b- 58,800.00 150-$ 58,650.00 Effective mortgage amount (into PV). ¼ 0.98 Monthly interest rate (calculated). 12§ 11.
Section 12: Real Estate and Lending 127 Example 1: A lender wishes to induce the borrower to prepay a low interest rate loan. The interest rate is 5% with 72 payments remaining of $137.17 and a balloon payment at the end of the sixth year of $2000. If the lender is willing to discount the future payments at 9%, how much would the borrower need to prepay the note? Keystrokes Display g fCLEARG 72n 72.00 Months (into n). 9gC 0.75 Discount rate (into i). 137.17P* 137.17 Monthly payments (into PMT).
Section 12: Real Estate and Lending Yield of a Mortgage Traded at a Discount or Premium The annual yield of a mortgage bought at a discount or premium can be calculated given the original mortgage amount, interest rate, and periodic payment, as well as the number of payment periods per year, the price paid for the mortgage, and the balloon payment amount (if it exists). Information is entered as follows: 1. Press g and fCLEARG. 2.
Section 12: Real Estate and Lending 129 Keystrokes Display 79000Þ$ –79,000.00 Input price of mortgage (into PV; negative to indicate money paid out). ¼ 0.97 Yield per month (calculated). 12§ 11.68 Percent annual yield. Example 2: Using the same information given in example 1, calculate the annual yield if the loan is to be paid in full at the end of the fifth year (from original issuance). (In this case both the payment amount and the balloon must be calculated since they are not given.
Section 12: Real Estate and Lending The Rent or Buy Decision The question of whether to rent or purchase a residence is not always easy to answer, especially when the time period over which you would own or rent a house is short. This program performs an analysis which could be helpful in reaching a decision. Essentially, it calculates a yield or rate of return on the proposed investment.
Section 12: Real Estate and Lending KEYSTROKES DISPLAY KEYSTROKES 131 DISPLAY 1 - 44- 11- 30 :5 45- $ 12- 13 - 46- :3 13- 45 gC 14- 43 12 + 48- 40 :2 15- 45 2 - 49- 30 gA 16- 43 11 Þ 50- 16 P 17- 14 P 51- 14 d 18- 33 :0 52- 45 0 d 19- 33 gA 53- 43 11 0 20- 0 :1 54- 45 1 n 21- 11 :6 55- 45 6 :0 22- 0 + 56- 40 1 23- 1 Þ 57- 16 2 24- 2 $ 58- 13 § 25- 20 ¼ 59- 12 f! 26- 11 :gC 60-45 d 27- 33 t 61- d 28- 33 :9 62- 45
Section 12: Real Estate and Lending REGISTERS n: Period i: Apprec. PV: Price PMT: Used FV: Used R0: Period R1: Dwn Pmt R2: Life R3: i(Mtg) R4: Taxes/Mo R5: Improve. R6: Closing C. R7: % Comm. R8: Rent R9: Savings i R.0: Bracket R.1: Unused. 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.
Section 12: Real Estate and Lending 133 16. Press t to compute the yield on your investment in the house.* 17. Press t to compute the value of a savings account or other investment. 18. Compare the value of the hypothetical savings account to the net proceeds of the sale of the house. Examine the sign and magnitude of the yield to arrive at your decision. 19. To change data and repeat the calculations, store the changed values in the appropriate registers and go to step 12.
Section 12: Real Estate and Lending Keystrokes Display 4n 4.00 Years in investment. 10¼ 10.00 Yearly appreciation rate. 70000$ 70,000.00 House price. t 32,391.87 NCPR (calculated). t 19.56 Yield. t 21,533.79 Balance in savings. By purchasing a house, you would gain $10,858.08 (32,391.87 – 21,533.79) over an alternate investment at 6.25% interest.
Section 12: Real Estate and Lending 135 Leases often call for periodic contractual adjustments of rental payments. For example, a 2-year lease calls for monthly payments (at the beginning of the month) of $500 per month for the first 6 months, $600 per month for the next 12 months, and $750 per month for the last 6 months. This situation illustrates what is called a “step-up” lease. A “step-down” lease is similar, except that rental payments are decreased periodically according to the lease contract.
Section 13 Investment Analysis Partial-Year Depreciation For both income tax purposes and financial analyses, it is valuable to calculate depreciation based on a calendar or fiscal accounting year. When the acquisition date of an asset does not coincide with the start of the year — which is the rule rather than the exception — the amounts of depreciation in the first and last years are computed as fractions of a full year’s depreciation.
Section 13: Investment Analysis KEYSTROKES DISPLAY KEYSTROKES 137 DISPLAY ?3 14- 44 3 gu 36- 43 31 :$ 15- 45 13 :$ 37- 45 13 ~ 16- 34 :M 38- 45 15 - 17- 30 - 39- $ 18- 13 :3 40- 45 3 :n 19- 45 11 gi30 41-43, 33 30 :1 20- 45 1 fs 30 REGISTERS n: Life i: Unused PV: Dep. Value PMT: Unused FV: Salvage R0: Used R1: #Mos./12 R2: Counter st R3: 1 Yr. Dep. R4–R.4: Unused 1. Key in the program. 2. Press fCLEARG. 3. Key in the book value then press $. 4.
Section 13: Investment Analysis Note: If the number of months in the first calendar year is less than 12, the amount of depreciation in the 1st year will be less than a full year’s depreciation. The actual number of years that depreciation will occur is equal to the life +1. For example, a drill has a life of 3 years and is purchased 3 months before the year end. The following time diagram shows that depreciation will occur over 4 calendar years.
Section 13: Investment Analysis Keystrokes Display 25n 25.00 Life. 25\ 25.00 Year desired. 4t 25.00 5,000.00 3,333.33 Twenty-fifth year: depreciation, remaining depreciable value. 26.00 3,333.33 0.00 Twenty-sixth year: depreciation, remaining depreciable value. ~ t ~ 139 Example 2: A new car was purchased for $6,730 with 41/2 months remaining in the year.
Section 13: Investment Analysis KEYSTROKES DISPLAY 1 07- - 08- ?0 09- 1 10- f# 11- 42 :1 12- 45 § 13- ?3 14- 44 :$ 15- 45 ~ KEYSTROKES 1 1 44 DISPLAY 27- 1 30 ?+0 28-44 40 0 0 ?+2 29-44 40 2 1 gi22 30-43, 33 22 25 :2 31- 45 2 1 gu 32- 43 31 20 :$ 33- 45 13 3 :M 34- 45 15 13 - 35- 16- 34 :3 36- 45 3 - 17- 30 gi26 37-43, 33 26 $ 18- 13 fs 30 REGISTERS n: Life i: Factor PV: Dep. Value PMT: Unused FV: Salvage R0: Used R1: #Mos.
Section 13: Investment Analysis 141 remaining depreciable value. If desired, press :$:3=~-:M- to find the total depreciation through the current year. 9. Press t for the amount of depreciation then, if desired, press ~ for the remaining depreciable value for the next year. Repeat this step for the following years. 10. For a new case press gi00 and return to step 2. Example: An electron beam welder which costs $50,000 is purchased 4 months before the end of the accounting year.
Section 13: Investment Analysis KEYSTROKES DISPLAY ?2 06- 44 1 07- - 08- ?0 09- 1 10- fÝ 11- 42 :1 12- 45 § 13- ?3 14- 44 :$ 15- 45 ~ 44 KEYSTROKES DISPLAY 2 :0 28- 45 0 1 fÝ 29- 42 24 30 t 30- 31 0 1 31- 1 1 ?=0 32-44 40 0 24 ?=2 33-44 40 2 34-43, 33 26 1 gi26 20 :2 35- 45 2 3 gu 36- 43 31 13 :$ 37- 45 13 16- 34 :M 38- 45 15 - 17- 30 - 39- $ 18- 13 :3 40- 45 3 :n 19- 45 11 gi30 41-43, 33 30 :1 20- 45 1 fs 30 R
Section 13: Investment Analysis 143 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 :$:3= ~-:M- to find the total depreciation through the current year. 8. Press t for the amount of depreciation then, if desired, press ~ for the remaining depreciable value for the next year. Repeat this step for the following years. 9.
Section 13: Investment Analysis Full- and Partial-Year Depreciation with Crossover When calculating declining-balance depreciation it is often advantageous for tax purposes to switch from declining balance to straight-line depreciation at some point. This hp 12c program calculates the optimum crossover point and automatically switches to straight-line depreciation at the appropriate time.
Section 13: Investment Analysis KEYSTROKES DISPLAY KEYSTROKES § 17- ?1 18- 44 1 :$ 19- 45 ~ 145 DISPLAY n 66- 11 0 67- 0 13 ?6 68- 20- 34 1 69- - 21- 30 ?-2 70-44 30 2 $ 22- 13 ?=0 71-44 40 0 \ 23- 36 :5 72- 45 5 gF 24- 36 ?-1 73-44 30 1 ~ 25- 34 :3 74- 45 3 :M 26- 15 fV 75- 42 23 - 27- 30 ?+1 76-44 40 1 ~ 28- 34 1 77- :0 29- 0 ?-0 78-44 30 0 1 30- 1 ?+2 79-44 40 2 go 31- 43 34 ?+3 80-44 40 3 gi39 32-43
Section 13: Investment Analysis KEYSTROKES DISPLAY KEYSTROKES DISPLAY ?+1 43-44 40 1 :6 92- 45 6 ?5 44- 44 5 gm 93- 43 35 :$ 45- 45 13 gi74 94-43, 33 74 :M 46- 45 15 gi58 95-43, 33 58 - 47- 30 fs 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.
Section 13: Investment Analysis 147 Example: An electronic instrument is purchased for $11,000, with 6 months remaining in the current fiscal year. The instrument’s useful life is 8 years and the salvage value is expected to be $500. Using a 200% declining-balance factor, generate a depreciation schedule for the instrument’s complete life. What is the remaining depreciable value after the first year? What is the total depreciation after the 7th year? Keystrokes Display fCLEARH 0.00 11000$ 11,000.
Section 13: Investment Analysis Excess Depreciation When accelerated depreciation is used, the difference between total depreciation charged over a given period of time and the total amount that would have been charged under straight-line depreciation is called excess depreciation. To obtain excess depreciation: 1. 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 149 This Modified Internal Rate of Return procedure (MIRR) is one of several IRR alternatives which avoids the drawbacks of the traditional IRR technique. The procedure eliminates the sign change problem and the reinvestment (or discounting) assumption by utilizing user stipulated reinvestment and borrowing rates. Negative cash flows are discounted at a safe rate that reflects the return on an investment in a liquid account.
Section 13: Investment Analysis Keystrokes Display 10gCfl 657,152.37 NPV of positive cash flows. 775,797.83 NFV of positive cash flows. 6gCfl -660,454.55 NPV of negative cash flows. 20n¼ 0.81 Monthly MIRR 12§ 9.70 Annual MIRR. Þ$ 20nM 180000ÞgJ 0gK5ga 100000ÞK 5ga File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 150 of 209 Printered Date: 2005/7/29 Dimension: 14.
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 If solving for the payment amount will be done repetitively, key in the following hp 12c program. KEYSTROKES DISPLAY KEYSTROKES fs DISPLAY 1 09- 1 Þ 10- 16 fCLEARÎ 00- g 01- 43 8 P 11- 14 fCLEARG 02- 42 34 $ 12- 13 :0 03- 45 0 :1 13- :1 04- 45 1 + 14- - 05- 30 :3 15- n 06- 11 ~ 16- 34 :2 07- z 17- 10 ¼ 08- 45 2 12 45 1 40 45 3 fs REGISTERS n: n–#Adv. Pmt. i: i PV: Used PMT: –1 FV: 0 R0: n R1: #Adv. Pmt.
Section 14: Leasing 153 Example 2: Using the preceding program, solve for the monthly payment using the information given in example 1. Then change the yearly interest to 15% and solve for the new payment amount. Keystrokes Display 12?0 12.00 Duration of lease. 3?1 3.00 Number of advance payments. ?2 0.83 Periodic interest rate. 750?3t 64.45 Monthly payment to be received. 65.43 Monthly payment to achieve a 15% yield.
Section 14: Leasing Solving for Yield To calculate the periodic yield, information is entered as follows: 1. Press g and fCLEARG. 2. Key in the total number of payments in the lease then press \. 3. Key in the total number of payments made in advance then press ?0-n. 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. Example 1: A lease has been written to run for 60 months.
Section 14: Leasing 155 If solving for yield will be done repetitively, key in the following hp 12c program: KEYSTROKES DISPLAY KEYSTROKES fs DISPLAY :3 09- 45 3 Þ 10- :1 11- 45 1 :P 12- 45 14 fCLEARÎ 00- g 01- 43 8 fCLEARG 02- 42 34 :0 03- 45 0 § 13- 20 :1 04- 45 1 + 14- 40 - 05- 30 $ 15- 13 n 06- 11 ¼ 16- 12 :2 07- :gC 17-45, 43 12 P 08- 45 2 14 16 fs REGISTERS n: n–#Adv. Pmts. i: i PV: Used PMT: Pmt. FV: 0 R0: n R1: Adv. Pmts.
Section 14: Leasing Keystrokes Display 25000?3t 17.33 Annual yield (as a percentage). 625?2t 19.48 Annual yield (as a percentage) when PMT is increased $25. Advance Payments With Residual Situations may arise where a transaction has advance payments and a residual value (salvage value) at the end of the normal term. Solving for Payment The following program solves for the periodic payment amount necessary to achieve a desired yield.
Section 14: Leasing 157 REGISTERS n: Used. i: Interest PV: Used PMT: –1. FV: Residual R0: # Pmts (n) R1: Interest. R2: Loan. R3: Residual R4: # Adv. Pmt. R5: Used R6–R.6: Unused 1. Key in the program. 2. Key in the total number of payments then press ?0. 3. Key in or calculate the periodic interest rate then press ?1. 4. Key in the loan amount then press ?2. 5. Key in the residual value then press ?3. 6. Key in the total number of payments made in advance then press ?4.
Section 14: Leasing Example 2: Using the information from example 1, what would the monthly payments be if the lessor desired a yield of 18% annually? Keystrokes Display 487.29 From previous example. 18\12z 1.50 Monthly interest rate. ?1t 520.81 Monthly payment received by lessor. 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.
Section 14: Leasing 159 Keystrokes Display §=gJ –4,710.00 Net amount of cash advanced. 145gK34ga 34.00 Thirty-four cash flows of $145.00. 0gK 0.00 Thirty-fifth cash flow. 1500gK 1,500.00 Thirty-sixth cash flow. fL12§ 18.10 Annual yield to lessor. File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 159 of 209 Printered Date: 2005/7/29 Dimension: 14.
Section 15 Savings Nominal Rate Converted to Effective Rate Given a nominal interest rate and the number of compounding periods per year, this keystroke procedure computes the effective annual interest rate. 1. Press g and fCLEARG. 2. Key in the annual nominal rate as a percentage, then press \. 3. Key in the number of compounding periods per year, then press nz¼. 4. Key in 100 then press Þ\$. 5. Press M+ to obtain the effective annual interest rate.
Section 15: Savings 161 REGISTERS n: # Periods. i: Nom. Rate/n FV: Eff. Rate R0–R.9: Unused PV: 0 PMT: Used. 1. Key in the program. 2. Key in the annual nominal rate as a percentage then press \. 3. Key in the number of compounding periods per year then press t to obtain the effective annual interest rate. 4. For a new case return to step 2. Example 2: What is the effective annual rate of interest if the annual nominal rate of 51/4% is compounded monthly? Keystrokes Display 5.25\ 12t 5.
Section 15: Savings Nominal Rate Converted to Continuous Effective Rate This procedure converts a nominal annual interest rate to the continuous effective rate. 1. Press 1\. 2. Key in the nominal rate as a percentage then press b. 3. Press g>à. Example: What is the effective rate resulting from a 51/4% passbook rate with continuous compounding? Keystrokes Display 1\5.25b g> 1.05 à 5.39 Continuous rate.
Section 16 Bonds 30/360 Day Basis Bonds A bond is a contract to pay interest, usually semiannually, at a given rate (coupon) and to pay the principal of the bond at some specified future date. A bond which is calculated on a 30/360 day basis is one in which the day count basis is computed using 30 days in a month and 360 days in a year.
Section 16: Bonds KEYSTROKES DISPLAY KEYSTROKES d 14- 33 1 15- 8 DISPLAY d 39- 1 :1 40- 16- 8 + 41- 40 0 17- 0 Þ 42- 16 z 18- 10 $ 43- 13 n 19- 11 ¼ 44- 12 gT 20- 24 2 45- 2 1 21- 1 § 46- 20 ~ 22- 34 - 23- 30 43 33 45 1 fs REGISTERS n: ∆ days/180 i: Yield/2 PV: Price PMT: Coupon/2. FV: Red+Cpn./2 R0: Yield R1: Price. R2: Coupon R3: Dset R4: Dmat R5: Redemption R6: Coupon/2. R7–R.3: Unused 1. Key in the program. 2.
Section 16: Bonds 165 For a new case return to step 3. Note that only those values which have been changed need to be reentered and stored. 8. If yield is desired: a. Press 0?0. b. Key in the price as a percentage of par value and press ?1. c. Press t to compute annual yield to maturity. 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 Annual Coupon Bonds For bonds which have annual coupons, use the following hp 12c program to evaluate price and accrued interest on an Actual/Actual day basis. This program may be modified for annual coupon bonds to be calculated on a 30/360 day basis.
Section 16: Bonds 167 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 (making the program two steps longer). 1. Key in the program and press ?É if the C status indicator is not displayed. 2. Key in the total number of coupons which are received and press ?0. 3.
Appendixes File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 169 of 209 Printered Date: 2005/7/29 Dimension: 14.
Appendix A The Automatic Memory Stack Four special registers in the hp 12c are used for storing numbers during calculations. To understand how these registers are used, they should be visualized as stacked on top of each other. (For this reason, they are generally referred to as the “stack registers” or collectively as “the stack.”) The stack registers are designated X, Y, Z, and T.
Appendix A: The Automatic Memory Stack 171 Now let’s see what happens in the stack during a chain calculation: (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: The Automatic Memory Stack Termination of Digit Entry The first digit keyed in after digit entry has been terminated replaces the number already in the displayed X-register. Digit entry is automatically terminated when any key is pressed (except for digit entry keys — digit keys,., Þ, and É — and prefix keys — 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: The Automatic Memory Stack 173 Pressing d four times successively displays the numbers in the Y-, Z-, and T-registers and returns the numbers to their original registers. One-Number Functions and the Stack One-number mathematics and number-alteration functions — y, r, °, >, e, B, Ñ, and T — use only the number in the displayed X-register. When the key is pressed, the function is performed upon the number in the X-register, and the answer is then placed into the X-register.
Appendix A: The Automatic Memory Stack When an arithmetic operation or q is performed, the answer is placed in the X-register, the number formerly in the X-register is copied into the LAST X register, and the stack drops. When the stack drops, the number in the Z-register is copied into the Y-register, and the number in the T-register is copied into the Z-register but also remains in the T-register. The diagram on the next page illustrates the stack operation when 8 ÷ 2 is calculated.
Appendix A: The Automatic Memory Stack 175 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: The Automatic Memory 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, _, ^, A, or C was the last key pressed, as described on page 172), 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: The Automatic Memory Stack 177 The diagram on page 171 illustrates how the automatic stack lift and stack drop make chain calculations quick and error-free. Virtually every chain calculation you are likely to encounter can be done using only the four stack registers.
Appendix A: The Automatic Memory Stack Keystrokes 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 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 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 B: More About L Your guess will aid the calculator in its search, and if it finds an IRR answer near your guess, that answer will be displayed. Since the calculator cannot tell you the number of solutions that exist when there is more than one mathematically correct answer, you can continue to make guesses, pressing :gt after each one, to search for IRR solutions. You can hasten this process by using the l function to help you make a good guess.
Appendix C Error Conditions Some calculator operations cannot be performed under certain conditions (for example, z when x = 0). If you attempt such an operation under these conditions, the calculator will display the word Error followed by a digit, 0 through 9. Listed below are operations that cannot be performed under the conditions specified. The symbols x and y represent the number in the X- and Y-registers, respectively, when the operation key is pressed.
Appendix C: 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 B.
Appendix C: Error Conditions 183 Error 5: Compound Interest Operation Condition n PMT ≤ –PV × i PMT = FV × i i ≤ –100 The values in i, PV, and FV are such that no solution exists for n. ¼ PMT = 0 and n < 0 Cash flows all have same sign. $ i ≤ –100 P n=0 i=0 i ≤ –100 M i ≤ –100 ! x≤0 x is noninteger. l i ≤ –100 V n≤0 n > 1010 x≤0 x is noninteger Ý # Error 6: Storage Registers Operation Condition ? Storage register specified does not exist or has been converted to program lines.
Appendix C: Error Conditions Error 7: IRR Refer to Appendix B. 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 E.
Appendix D 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 D: 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 D: Formulas Used 187 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 D: Formulas Used Bonds Reference: Spence, Graudenz, and Lynch, Standard Securities Calculation Methods, Securities Industry Association, New York, 1973. 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. = E – DCS = days from settlement date to next 6–month coupon date.
Appendix D: Formulas Used Depreciation L = asset’s useful life expectancy. SBV = starting book value. SAL = salvage value. FACT j = declining-balance factor expressed as a percentage. = period number. DPNj = depreciation expense during period j. RDVj = remaining depreciable value at end of period j = RDVj–1 – DPNj where RDV0 = SBV – SAL RBVj = remaining book value = RBVj–1 – DPNj where RBV0 = SBV Y1 = number of months in partial first year.
Appendix D: Formulas Used Program for partial year: ⎛ L ⎞ ⎛ Y1 ⎞ DPN1 = ⎜ ⎟ ⋅ ⎜ ⎟ ⋅ (SBV − SAL ) ⎝ SOYD ⎠ ⎝ 12 ⎠ ⎛ LADJ − j + 2 ⎞ ⎟ ⋅ (SBV − D1 − SAL ) for j ≠ 1 DPN j = ⎜⎜ ⎟ ⎝ SOYDLADJ ⎠ ⎛ Y1 ⎞ ⎟ where LADJ = L − ⎜ ⎝ 12 ⎠ Declining-Balance Depreciation Keyboard function: DPN j = RBVj −1 ⋅ FACT for j = 1, 2, …, L 100L Program for partial first year: FACT Y1 ⋅ 100L 12 FACT DPN j = RBVj −1 ⋅ for j ≠ 1 100L DPN1 = SBV ⋅ Modified Internal Rate of Return n = number of compounding periods.
Appendix D: Formulas Used Interest Rate Conversions C = number of compounding periods per year. EFF = the effective annual interest rate as a decimal. NOM = the nominal annual interest rate as a decimal.
Appendix D: Formulas Used r= ⎡ ⎢∑ xy − ⎣ ⎡ 2 ⎢∑ x − ⎣⎢ ∑ 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 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 ob
Appendix E Battery, Warranty, and Service Information Battery The hp 12c is shipped with one 3 Volt CR2023 Lithium battery. Battery life depends on how the calculator is used. If the calculator is being used to perform operations other than running programs, it uses much less power. Low-Power Indication A battery symbol (¼) shown in the upper-left corner of the display when the calculator is on signifies that the available battery power is running low.
Appendix E: Battery, Warranty, and Service Information To install a new battery, use the following procedure: 1. With the calculator turned off, slide the battery cover off. 2. Remove the old battery. 3. Insert a new battery, with positive polarity facing outward. 4. Replace the battery cover. Note: Be careful not to press any keys while the battery is out of the calculator.
Appendix E: Battery, Warranty, and Service Information 195 the ¼ battery power indicator) should turn on.* If the display shows Error 9, goes blank, or otherwise does not show the proper result, the calculator requires service.† 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.
Appendix E: Battery, Warranty, and Service Information Warranty hp 12c Financial Calculator; Warranty period: 12 months 1. HP warrants to you, the end-user customer, that HP hardware, accessories and supplies will be free from defects in materials and workmanship after the date of purchase, for the period specified above. 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 E: Battery, Warranty, and Service Information 197 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 E: Battery, Warranty, and Service Information Asia Pacific Country : Australia Singapore L.America Country : Argentina Brazil Mexico Venezuela Chile Columbia Peru Central America & Caribbean Guatemala Puerto Rico Costa Rica N.
Appendix E: Battery, Warranty, and Service Information 199 Regulatory Information This section contains information that shows how the hp 12c financial calculator complies with regulations in certain regions. Any modifications to the calculator not expressly approved by Hewlett-Packard could void the authority to operate the 12c in these regions. USA This calculator generates, uses, and can radiate radio frequency energy and may interfere with radio and television reception.
Appendix E: Battery, Warranty, and Service Information Disposal of Waste Equipment by Users in Private Household in the European Union This symbol on the product or on its packaging indicates that this product must not be disposed of with your other household waste. Instead, it is your responsibility to dispose of your waste equipment by handing it over to a designated collection point for the recycling of waste electrical and electronic equipment.
Appendix F United Kingdom Calculations The calculations for most financial problems in the United Kingdom are identical to the calculations for those problems in the United States — which are described earlier in this handbook. Certain problems, however, require different calculation methods in the United Kingdom than in the United States, even though the terminology describing the problems may be similar.
Appendix F: United Kingdom Calculations Annual Percentage Rate (APR) Calculations In the United Kingdom, the calculation of the Annual Percentage Rate of Charge (APR) in accordance with the United Kingdom Consumer Credit Act (1974) differs from the calculation of the APR in the United States.
Function Key Index General ; Power on /off key (page 16). f Shift key. Selects alternate function in gold above the function keys (page 16). Also used in display formatting (page 71). g Shift key. Selects alternate function in blue on the slanted face of the function keys (page 16). CLEARX after f, g, ?, : or i, cancels that key (page 18). fCLEARX also displays mantissa of number in the displayed X-register (page 73). Digit Entry \ Enters a copy of number in displayed X-register into Y-register.
Function Key Index Financial CLEAR G Clears contents of financial registers (page 33). × Sets payment mode to Begin for compound interest calculations involving payments (page 37). Â Sets payment mode to End for compound interest calculations involving payments (page 37). Ï Calculates simple interest (page 33). w Stores or computes number of periods in financial problem (page 32). A Multiplies a number in displayed X-register by 12 and stores the resulting value in the n-register (page 39).
Function Key Index Ö Computes mean Mathematics (average) of x-values and r Computes square root y-values using of number in displayed accumulated statistics X-register (page 83). (page 77). q Raises number in Computes weighted Y-register to power of average of y-(item) and number in X-register x-(weight) values using (page 85). accumulated statistics (page 81). v Computes sample standard deviations of xand y-values using accumulated statistics (page 79).
Programming Key Index s Program/Run. Toggles into and out of Program mode. Automatically sets program to line 00 when returning to Run mode (page 86). N Memory map. Describes the current allocation of memory; the number of lines allotted to program memory and the number of available data registers (page 93). 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 Run Mode Active Keys: Pressed from keyboard: t Run/Stop. Begins execution of a stored program. Stops execution if program is running (page 89). i Go to. Followed by a decimal point and a two-digit number, positions calculator to that line in program memory. No instructions are executed (page 95) i Go to. Followed by a two-digit number, positions calculator to that line in program memory. No instructions are executed (page 103). Ç Single step.
Subject Index Bonds, municipal, 67 Bonds, state and local government, 67 Bonds, U.S. Treasury, 66 Branching, 103–12, 116 Branching, adding instructions by, 116–19 Branching, conditional, 107–8 Branching, simple, 103 A , 12, 54, 172 Adding instructions, 114–19 Advance payments, 151, 156 Amortization, 38, 54–56, 186 Annual interest rate, 39 Annual Percentage Rate, 52–53, 124–26, 202 Annuities, 36 Annuities, deferred, 134–35 Annuity due, 37–38 Appreciation, 38 APR.
Subject Index Compound interest, 39–53, 186 Compound interest calculation, 11 Compounding periods, 34, 39 Conditional branching, 107–8 Conditional test instructions, 107 Constants, arithmetic calculations with, 177 Constants, arithmetic calculations with, 75 Continuous compounding, 162, 191 Continuous effective rate, 162 Continuous memory, 70 Continuous memory, resetting of, 33, 37, 70, 72, 93, 94 D , 29–31 , 68, 172 , 51, 172 D.
Subject Index Interest, simple, 33 Internal rate of return, 57 Internal rate of return, calculating, 63 Internal rate of return, modified, 148 Interrupting a program, 97 IRR, 57, 148 K Keyboard, 16 L , 74 LAST X register, 70 Leasing, 151 Linear estimation, 80 Logarithm, 83 Looping, 103 Low-power indicator, 16 M , 172 Mantissa, 18, 73 Mantissa Display Format, 73 Mean, 77 Mean, weighted, 81 memory, 23 Memory, program, 94 Modified internal rate of return, 148 Mortgage, price of, 126 Mortgage, yield of,
Subject Index Program, running one line at a time, 94 Program, stopping, 97, 101 Program, storing, 120 Programming, 88 Programs, multiple, 120 PV, 36 R , 83 Reciprocal, 83 registers, 23 Registers, financial, 32 Registers, statistics, 76 Renting versus Buying, 130 Residual, 156 Round, 83 Rounding, 71 Running message, 12, 63 Square Root, 83 Stack, 170 Standard deviation, 79 Statistics, 76 Status indicators, 71 Storage register arithmetic, 24 Storage registers, clearing, 24 Storing numbers, 32 Storing progr
