About This Handbook This HP 12C Platinum Owner’s Handbook and Problem-Solving Guide is intended to help you get the most out of your investment in your HP 12C Platinum Programmable Financial Calculator. Although the excitement of acquiring this powerful financial tool may prompt you to set this handbook aside and immediately begin “pressing buttons,”...
For More Solutions to Financial Problems In addition to the specialized solutions found in Sections 12 through 16 of this handbook, many more are available in the optional HP 12C Platinum Solutions Handbook. Included are solutions to problems in lending, forecasting, pricing, statistics, savings, investment analysis, personal finance, securities, Canadian mortgages, learning curves in manufacturing, and queuing theory.
Contents Introduction ..................2 About This Handbook ..................2 Financial Calculations in the United Kingdom ..........3 For More Solutions to Financial Problems............3 Part I: Problem Solving..........15 Section 1: Getting Started ..............16 Power On and Off..................16 Low-Power Indication ................16 The Keyboard ....................
Contents Compound Interest Calculations ..............41 Specifying the Number of Compounding Periods and the Periodic Interest Rate ................... 41 Calculating the Number of Payments or Compounding Periods .... 41 Calculating the Periodic and Annual Interest Rates ....... 45 Calculating the Present Value ..............46 Calculating the Payment Amount ............
Contents Part II: Programming............85 Section 8: Programming Basics............86 Why Use Programs? ..................86 Creating a Program ..................86 Running a Program ..................87 Program Memory..................88 Identifying Instructions in Program Lines..........89 Displaying Program Lines............... 90 000 Instruction and Program Line 000........91 Expanding Program Memory..............
Contents Section 14: Leasing ................148 Advance Payments..................148 Solving For Payment ................148 Solving for Yield..................150 Advance Payments With Residual ............. 152 Solving for Payment ................152 Solving For Yield .................. 154 Section 15: Savings................156 Nominal Rate Converted to Effective Rate..........156 Effective Rate Converted to Nominal Rate..........
Contents Appendix G: United Kingdom Calculations ........ 203 Mortgages....................203 Annual Percentage Rate (APR) Calculations ..........203 Bond Calculations..................204 Function Key Index ..............205 Programming Key Index ............. 208 Subject Index ................211...
To install new batteries, refer to Appendix F. If you are not familiar with the use of an HP calculator keyboard, refer to the description on pages 16 and 17.
Making Financial Calculations Easy 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.) During these calculations, the word running flashes in the display to let you know that the calculator is running.
0.42 12§ Annual interest rate. 5.01 This is only a small sampling of the many financial calculations that can now be done easily with your HP 12C Platinum. To begin learning about this powerful financial tool, just turn the page.
Appendix F. The Keyboard Many keys on the HP 12C Platinum perform two or even three functions. The primary function of a key is indicated by the characters printed in white on the upper face of the key. The alternate function(s) of a key are indicated by the characters printed in gold above the key and the characters printed in blue on the lower face of the key.
Section 1: Getting Started appropriate prefix key (for example, “Pressing fL …”). References to the functions shown on the keyboard in gold under the bracket labeled “CLEAR” appear throughout this handbook preceded by the word “CLEAR” (for example, “The CLEAR H function …” or “Pressing fCLEARH …”). If you press the f or g prefix key mistakenly, you can cancel it by pressing fCLEAR X.
The CLEAR Keys Clearing a register or the display replaces the number in it with zero. Clearing program memory replaces the instructions there with gi000. There are several clearing operations on the HP 12C Platinum, as shown in the table below: Key(s) Clears: Display and X-register.
In RPN mode, any simple arithmetic calculation involves two numbers and an operation – addition, subtraction, multiplication, or division. To do such a calculation on your HP 12C Platinum, you first tell the calculator the two numbers, then tell the calculator the operation to be performed. The answer is calculated when the operation key (+,-,§, or z) is pressed.
The HP 12C Platinum is designed so that each time you press a function key in RPN mode, the calculator performs the operation then – not later – so that you...
Section 1: Getting Started Example: Suppose you’ve written three checks without updating your checkbook, and you’ve just deposited your paycheck for $1,053.00 into your checking account. If your latest balance was $58.33 and the checks were written for $22.95, $13.70, and $10.14, what is the new balance? Solution: When written down on paper, this problem would read 58.33 –...
5 and the 6 in step 2, the calculator was holding two numbers (12 and 5) inside for you, in addition to the 6 in the display. (The HP 12C Platinum can hold a total of three numbers inside, in addition to the number in the display.) After step 2, the calculator was still holding the 12 inside for you, in addition to the 30 in the display.
To check your understanding of how to calculate with your HP 12C Platinum, try the following problems yourself. Although these problems are relatively simple, more complicated problems can be solved using the same basic steps.
Section 1: Getting Started Storing and Recalling Numbers To store the number from the display into a data storage register: 1. Press ? (store). 2. Key in the register number: 0 through 9 for registers R through R , or .0 through .9 for registers R through R Similarly, to recall a number from a storage register into the display, press :...
Suppose you wanted to perform an arithmetic operation with the number in the display and the number in a storage register, then store the result back into the same register without altering the number in the display. The HP 12C Platinum enables you to do all this in a single operation.
Section 1: Getting Started Keystrokes Display 58.33?0 Stores the current balance in 58.33 register R 22.95?-0 Subtracts the first check from the 22.95 balance in R . Note that the display continues to show the amount subtracted; the answer is placed only in R 13.70?-0 Subtracts the second check.
\ before keying in the percentage – just as in a chain arithmetic calculation. Net Amount 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...
Section 2: Percentage and Calendar Functions the base amount inside after you calculate a percentage amount. To calculate a net amount, simply calculate the percentage amount, then press = or -. Example: You’re buying a new car that lists for $13,250. The dealer offers you a discount of 8%, and the sales tax is 6%.
Europe had nearly 30% of the total 29.69 sales. The HP 12C Platinum holds the total amount inside after a percent of total is calculated. Therefore, to calculate what percentage another amount is of the total: 1. Clear the display by pressing O.
29.69 sales. Calendar Functions The calendar functions provided by the HP 12C Platinum – D and Ò – can handle dates from October 15, 1582 through November 25, 4046. Date Format For each of the calendar functions – and also for bond calculations (E and S) –...
Section 2: Percentage and Calendar Functions For example, to key in April 7, 2004: Keystrokes Display 4.072004 4.07200 4 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.
(the extra days occurring in leap years), if any. In addition, the HP 12C Platinum also calculates the number of days between the two dates on the basis of a 30-day month. This answer is held inside the calculator;...
Section 2: Percentage and Calendar Functions Keystrokes Display gÕ Sets date format to month-day-year. 11.09 (Display shown assumes date remains from preceding example.) 6.032004\ Keys in earlier date and separates it 6.03 from the later date. 10.152005gÒ Keys in later date. Display shows 498.00 actual number of days.
Basic Financial Functions The Financial Registers In addition to the data storage registers discussed on page 23, the HP 12C Platinum has five special registers in which numbers are stored for financial calculations. These registers are designated n, i, PV, PMT, and FV. The first five...
Continuous Memory is reset (as described on page 70). Simple Interest Calculations The HP 12C Platinum simultaneously calculates simple interest on both a 360- day basis and a 365-day basis. You can display either one, as described below. Furthermore, with the accrued interest in the display, you can calculate the total amount (principal plus accrued interest) by pressing +.
Section 3: Basic Financial Functions basis. What is the amount of accrued interest he will owe you in 60 days, and what is the total amount owed? Keystrokes (RPN mode) Display If you have not altered the 60.00 7¼ numbers in the n, i, and PV 7.00 450Þ$ registers since the preceding...
Section 3: Basic Financial Functions oney paid out oney received Suppose you deposited (paid out) $1,000 into an account that pays 6% annual interest and is compounded monthly, and you subsequently deposited an additional $50 at the end of each month for the next 2 years. The cash flow diagram describing the problem would look like this: The arrow pointing up at the right of the diagram indicates that money is received at the end of the transaction.
Section 3: Basic Financial Functions payments in advance yield different results than calculations involving payments in arrears. Illustrated below are portions of cash flow diagrams showing payments in advance (Begin) and payments in arrears (End). In the problem illustrated in the cash flow diagram above, payments are made in arrears. egin Regardless of whether payments are made in advance or in arrears, the number of payments must be the same as the number of compounding periods.
Section 3: Basic Financial Functions ompound Growth Savings Plan Savings Account Pension Fund Appreciation Annuity Due ortgage ortgage With Balloon Direct Reduction (Installment) Loan Amortization Amortization Ordinary Annuity Ordinary Annuity ease Amortization Annuity Due ease With Buyback (Residual) Amortization Annuity Due...
Section 3: Basic Financial Functions Compound Interest Calculations Specifying the Number of Compounding Periods and the Periodic Interest Rate Interest rates are usually quoted at the annual rate (also called the nominal rate): that is, the interest rate per year. However, in compound interest problems, the interest rate entered into i must always be expressed in terms of the basic compounding period, which may be years, months, days, or any other time unit.
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.
Section 3: Basic Financial Functions 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 $325.
Section 3: Basic Financial Functions Keystrokes (RPN mode) Display fCLEARG Calculates and stores i. 6.25\24z¼ 0.26 775Þ$ Stores PV (with minus sign for cash –775.00 paid out). 50ÞP Stores PMT (with minus sign for –50.00 cash paid out). 4000M Stores FV. 4,000.00 gÂ...
Section 3: Basic Financial Functions In this example, M must be pressed twice, since the preceding key pressed was z. If we had stored the number of deposits in n (as we did following Example 1), we would have to press M only once here, since the preceding key pressed would have been w (as it was following Example 1).
Section 3: Basic Financial Functions Keystrokes (RPN mode) Display fCLEARG Calculates and stores n. 8\4§n 32.00 6000Þ$ –6,000.00 Stores PV (with minus sign for cash paid out). 10000M 10,000.00 Stores FV. ¼ Periodic (quarterly) interest rate. 1.61 4§ Annual interest rate. 6.44 Calculating the Present Value 1.
Section 3: Basic Financial Functions Keystrokes(RPN mode) Display fCLEARG Calculates and stores n. 48.00 15gC Calculates and stores i. 1.25 150ÞP Stores PMT (with minus sign for –150.00 cash paid out). gÂ Sets payment mode to End. –150.00 Maximum amount of loan. 5,389.72 1500+ Maximum purchase price.
Section 3: Basic Financial Functions Calculating the Payment Amount 1. Press fCLEARG to clear the financial registers. 2. Enter the number of payments or periods, using n or A. 3. Enter the periodic interest rate, using ¼ or C. 4. Enter either or both of the following: Present value, using $.
Section 3: Basic Financial Functions Keystrokes(RPN mode) Display fCLEARG 15\2§n Calculates and stores n. 30.00 9.75\2z¼ Calculates and stores i. 4.88 3200Þ$ Stores PV (with minus sign for cash –3200.00 paid out). 60000M 60,000.00 Stores FV. gÂ 60,000.00 Sets payment mode to End. Semiannual payment (with minus –717.44 sign for cash paid out).
Section 3: Basic Financial Functions Example 1: In Example 1 on page 48, we calculated that the payment amount on a 29-year, $43,400 mortgage at 14Ľ% annual interest is $523.99. If the seller requests a balloon payment at the end of 5 years, what would be the amount of the balloon? Keystrokes Display...
“odd first period”. For simplicity, in using the HP 12C Platinum we will always regard the first period as equal to the remaining periods, and we will refer to the period between the date interest...
Section 3: Basic Financial Functions period” or the “odd days”. (Note that the odd period is always assumed by the calculator to occur before the first full payment period.) The following two cash flow diagrams represent transactions including an odd period for payments in advance (Begin) and for payments in arrears (End).
Section 3: Basic Financial Functions must be divided by the number of days in a period. If interest is compounded monthly, for this number you can use either 30, 365/12, or (if the odd period falls entirely within a single month) the actual number of days in that month. Usually, a monthly period is taken to be 30 days long.
5.) This rounding affects the number inside the calculator as well as how the number appears in the display. The amounts calculated on your HP 12C Platinum may differ from those on the statements of lending institutions by a few cents, since different rounding techniques are sometimes used.
Section 3: Basic Financial Functions To obtain an amortization schedule: 1. Press fCLEARG to clear the financial registers. 2. Enter the periodic interest rate, using ¼ or C. 3. Enter the amount of the loan (the principal), using $. 4. Key in the periodic payment, then press ÞP (the sign of PMT must be negative, in accordance with the cash flow sign convention).
The number of payments keyed in just before f! is pressed is taken to be the payments following any that have already been amortized. Thus, if you now press 12f!, your HP 12C Platinum will calculate the amounts applied to interest and to the principal from the second year’s payments (that is, the second...
Section 3: Basic Financial Functions If you want to generate an amortization schedule but do not already know the monthly payment: 1. Calculate PMT as described on page 48. 2. Press 0n to reset n to zero. 3. Proceed with the amortization procedure listed on page 55 beginning with step 6.
Additional Financial Functions Discounted Cash Flow Analysis: NPV and IRR The HP 12C Platinum provides functions for the two most widely-used methods of discounted cash flow analysis: l (net present value) and L (internal rate of return). These functions enable you to analyze financial problems involving cash flows (money paid out or received) occurring at regular intervals.
Section 4: Additional Financial Functions A comparison of the NPV’s of alternative investment possibilities indicates which of them is most desirable: the greater the NPV, the greater the increase in the financial value of the investor’s assets. IRR is the rate of return at which the discounted future cash flows equal the initial cash outlay: IRR is the discount rate at which NPV is zero.
Section 4: Additional Financial Functions Note: The initial investment can not be zero. 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.
Calculating NPV for Grouped Cash Flows. A maximum of 30 cash flow amounts (in addition to the initial investment CF ) can be stored in the HP 12C Platinum. However, problems involving more than 30 cash flows can be handled if among the cash flows there are equal consecutive cash flows.
Section 4: Additional Financial Functions 3. If the initial investment consists of more than one cash flow of the amount entered in step 2, key in the number of those cash flows, then press ga. If ga is not pressed, the calculator assumes that N is 1.
Section 4: Additional Financial Functions Keystrokes Display Number of times this cash flow 3.00 amount occurs consecutively. 9100gK Next cash flow amount. 9,100.00 9000gK Next cash flow amount. 9,000.00 Number of times this cash flow 2.00 amount occurs consecutively. 4500gK Next cash flow amount.
Section 4: Additional Financial Functions finding IRR are extremely complex, involving a series of iterations – that is, a series of successive calculations. In each iteration, the calculator uses an estimate of IRR as the interest rate in a computation of NPV. The iterations are repeated until the computed NPV reaches about zero.
Section 4: Additional Financial Functions in the n register. For example, to display the fifth cash flow amount and the number of times that amount occurs consecutively: Keystrokes Display 9,000.00 Stores the value of j in the n 5.00 register. 2.00 Resets the number in the n register 7.00...
Section 4: Additional Financial Functions Changing Cash Flow Entries To change a cash flow amount: 1. Key the amount into the display. 2. Press ?. 3. Key in the number of the register containing the cash flow amount to be changed.
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 E and S calculations are done assuming a semiannual coupon payment and using an actual/actual basis (such as for U.S.
6.042017 Bond yield 8.15 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.
Section 4: Additional Financial Functions 6. Press: fV for depreciation using the straight-line method. fÝ for depreciation using the sum-of-the-years digits method. f# for depreciation using the declining-balance method. V, Ý, and # each place the amount of depreciation in the display. To display the remaining depreciable value (the book value less the salvage value) after the depreciation has been calculated, press ~.
Section 5: Additional Operating Features Section 5 Additional Operating Features Continuous Memory The calculator’s Continuous Memory contains the data storage registers, the financial registers, the stack and LAST X registers, program memory, and status information such as display format, date format, and payment mode. All information in Continuous Memory is preserved even while the calculator is turned off.
19.87 14.87 Although you see only two decimal places, all calculations in your HP 12C Platinum are performed with full 10-digit numbers..b u t t h e s e d i g i t s a re o u s e e o n l y t h e s e d i g i t s .
Section 5: Additional Operating Features Keystrokes Display 14.8746 14.9 Although nine decimal places were 14.87456320 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;...
Section 5: Additional Operating Features To set the display format to scientific notation, press f.. For example (assuming the display still shows 14.87456320 from the preceding example): Keystrokes Display 1.487456 01 The exponent in this example indicates that the decimal point should be moved one decimal place to the right, giving the number 14.87456, which is the first seven digits of the number previously in the display.
Section 5: Additional Operating Features If a calculation results in a number whose magnitude is less than 10 , the calculation is not halted, but the value 0 is used for that number in subsequent calculations. Errors. If you attempt an improper operation – such as division by zero – the calculator will display the word Error followed by a digit (0 through 9).
Section 5: Additional Operating Features Arithmetic Calculations With Constants Example: At Permex Pipes a certain pipe fitting is packaged in quantities of 15, 75, and 250. If the cost per fitting is $4.38, calculate the cost of each package. Keystrokes (RPN mode) Display Keys first quantity into calculator.
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 R , through R (These registers are therefore referred to as the “statistics registers.”)
Section 6: Statistics Functions Register Statistic (and display) n: number of data pairs accumulated. Σx: summation of x-values. Σx : summation of squares of x-values. Σy: summation of y-values. Σy summation of squares of y-values. Σxy: summation of products of x-values and y-values.
Standard deviation of sales. 4,820.59 Standard deviation of hours worked. 6.03 The formulas used in the HP 12C Platinum for calculating s , and s give best estimates of the population standard deviation based on a sample of the population. Thus, current statistical convention calls them sample standard deviations.
Section 6: Statistics Functions Example: Using the accumulated statistics from the preceding problem, estimate the amount of sales delivered by a new salesperson working 48 hours per week. Keystrokes Display 48gQ Estimated sales for a 48 hour 28,818.93 workweek. The reliability of a linear estimate depends upon how closely the data pairs would, if plotted on a graph, lie in a straight line.
Fourth item and weight. 4.00 Weighted mean cost per gallon. 1.19 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 Platinum Solutions Handbook.
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 Integer. Pressing gÑ replaces the number in the display by its integer portion – that is, it replaces each digit to the right of the decimal point by 0. The number is changed inside the calculator as well as in the display. The original number can be recalled to the display by pressing gF.
Section 7: Mathematics and Number-Alteration Functions The Power Function Pressing q calculates a power of a number – that is, y . Like the arithmetic function +, q requires two numbers: 1. Key in the base number (which is designated by the y on the key). 2.
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 (RPN mode) Display Keys in cost of item. 200. Separates cost of item from 200.00 percentage to be keyed in next. Amount of discount. 50.00 Price less discount. 150.00 Handling charge. Net cost (price less discount plus 155.00 handling charge).
Section 8: Programming Basics Example: Run the program created above to calculate the net cost of a typewriter listing for $625 and an executive chair listing for $159. Keystrokes (RPN mode) Display Sets calculator to Run mode. 155.00 Display shows number previously calculated.
Section 8: Programming Basics Identifying Instructions in Program Lines Each key on the HP 12C Platinum keyboard – except for the digit keys 0 through 9 – is identified by a two-digit “keycode” that corresponds to the key’s position on the keyboard. The first digit in the keycode is the number of the key row, counting from row 1 at the top;...
Occasionally you’ll want to check several or all of the instructions stored in program memory. The HP 12C Platinum enables you to review program instructions either forward or backward through program memory: Pressing Ê (single step) while the calculator is in Program mode advances the calculator to the next line in program memory, then displays that line number and the keycode of the instruction stored there.
Section 8: Programming Basics Program line 007 contains the last instruction you keyed into program memory. However, if you press Ê again, you’ll see that this is not the last line stored in program memory: Keystrokes Display Ê 008,43,33,000 Program line 008 As you should now be able to tell from the keycodes displayed, the instruction in program line 008 is gi000.
Section 8: Programming Basics program memory consists of 8 program lines, and there are 20 storage registers available for storage of data. rogram Memory Storage Registers As you key in a 310th instruction, storage register R is automatically converted into seven new lines of program memory. The instruction you key in is stored in program line 310, and the instruction i000 is automatically stored in program lines 311 through 316.
Section 8: Programming Basics To determine at any time how many program lines (including those containing i000) are currently in program memory and how many storage registers are currently available for conversion to program lines or for data storage, press gN (memory).
Section 8: Programming Basics For example, assuming the calculator is still in Program mode, you can set it to program line 000 as follows: Keystrokes Display gi.000 Program line 000 000, Executing a Program One Line at a Time Pressing Ê repeatedly with the calculator in Program mode (as described earlier) enables you to verify that the program you have stored is identical to the program you wrote –...
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: u (pause) and t (run/stop). Pausing During Program Execution When a running program executes a u instruction, program execution halts for about 1 second, then resumes.
Section 8: Programming Basics required amounts for the first item on the invoice manually. The keystroke sequence will use storage register arithmetic (described on page 25) in registers , and R to calculate the column sums. Since these registers are cleared when fCLEAR²...
Section 8: Programming Basics Keystrokes Display (RPN mode) 6.75?0 Stores tax rate in R 6.75 fCLEAR² Clears the registers in R through 0.00 Keys in quantity of item. Separates quantity of item from 13.00 cost of item to be keyed in next. 68.5 Keys in cost of item.
Section 8: Programming Basics Now, to run the program: Keystrokes Display (RPN mode) Sets calculator to Run mode. 950.61 fCLEAR² Clears registers R – R 0.00 6.75?0 Stores tax rate. 13\68.5 Enters quantity and price of first 68.5 item on invoice. AMOUNT for first item.
Section 8: Programming Basics Example: Replace the program above by one containing t instructions instead of u instructions. Keystrokes Display (RPN mode) Sets calculator to Program mode. 000, fCLEARÎ Clears program memory. 000, § 001, 31 Stops program execution to 002, display AMOUNT.
Section 8: Programming Basics Keystrokes Display (RPN mode) Sum of TOTAL column. 6,370.52 Program execution is also automatically halted when the calculator overflows (refer to page page 73) or attempts an improper operation that results in an Error display. Either of these conditions signifies that the program itself probably contains an error.
Section 9 Branching and Looping Although the instructions in a program normally are executed in order of their program line numbers, in some situations it is desirable to have program execution transfer or “branch” to a program line that is not the next line in program memory.
Section 9: Branching and Looping If you want to terminate the execution of a loop, you can include an o or m instruction (described below) or an t instruction within the loop. You can also terminate execution by pressing any key while the loop is being executed. Example: The following program automatically amortizes the payments on a home mortgage without requiring you to press f! for each payment.
Section 9: Branching and Looping Keystrokes Display gi002 007,43,33,002 Transfers program execution to line 002, so that the number of payments to be amortized can be recalled to the display before the ! instruction in line 003 is executed. Sets calculator to Run mode. 0.00 (Display shown assumes no results remain from previous...
Section 9: Branching and Looping Keystrokes Display Ê 0 Line 002: :0. Program 002, execution has branched to the beginning of the loop for the second pass through it. 1.00 Ê 11 Line 003: f!. 003, Portion of second month’s –531.12 payment applied to interest.
Section 9: Branching and Looping The HP 12C Platinum provides two conditional test instructions that are used in programs for conditional branching: o tests whether the number in the X-register (represented by the x in the key symbol) is less than or equal to the number in the Y-register (represented by the y in the key symbol).
Section 9: Branching and Looping rogram Execution rogram Execution If True If False rogram execution continues at line 004 rogram execution continues at line 007 Example: The following program calculates income tax at a rate of 20% on incomes of $20,000 or less and 25% on incomes of more than $20,000. To conserve program lines, the program assumes that the test value –...
Section 9: Branching and Looping Y-registers (as also explained in Appendix A): that is, it will place the income back into the X-register and place the test value into the Y-register. This is necessary because when either the :2 instruction in line 005 or the :1 instruction in line 007 is executed, the number in the X-register is moved into the Y-register;...
Section 9: Branching and Looping Keystrokes Display (RPN mode) 20000?0 Stores test value in register R 20,000.00 20?1 Stores 20% tax rate in register R 20.00 25?2 Stores 25% tax rate in register R 25.00 15000 Keys income less than test value 15,000.
Section 9: Branching and Looping Keystrokes Display (RPN mode) Ê 34 Line 003 go. 003, 20,000.00 Ê 004,43,33,007 Condition tested by o was true, so program execution continued with line 004: gi007. 20,000.00 Ê 1 Line 007: :1. 007, 20% tax rate has been recalled to 20.00 X-register, moving income to Y- register.
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;...
Section 10: Program Editing Keystrokes(RPN mode) Display Sets calculator back to Run mode. 6,250.00 (Display shown assumes results remain from last example in preceding section.) :2?6 Copies tax rate from R into R 25.00 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.
Section 10: Program Editing To add instructions within a program, you could simply key in the new instructions, beginning at the proper program line, followed by the original instructions from that program line through the end of the program. This method is described below under Adding Instructions by Replacement.
Section 10: Program Editing instruction (-) following the point at which the new instruction is being added, it is simplest to add the t instruction by replacement, as follows: Keystrokes Display (RPN mode) Sets calculator to Program mode. 000, gi.008 25 Sets calculator to last program 008, line to be executed, which...
Section 10: Program Editing i000 instruction remaining at the end of program memory), and it ensures that program execution will branch to line 000 after the program is run. 6. Key in the instruction(s) being added. 7. Key in the instruction that originally immediately followed the point at which the new instruction(s) are being added –...
Section 10: Program Editing Keystrokes Display (RPN mode) gi000 011,43,33,000 Ensures that i000 instruction follows program. 012, 013, Added instructions. 014, gi000 015,43,33,000 0 Keys in instruction immediately 016, following point at which new instructions are being added. (This instruction was replaced in line 001 by i012 instruction.) gi002 017,43,33,002 Branches back to second line (line...
Section 10: Program Editing ranches to line 012 000 instruction 1 1, 43,33, preserved 43,33, Instructions added 43,33, 43,33, Instruction replaced in line 001 43,33, 43,33, ranches back to line 002...
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.
Section 11: Multiple Programs Example 1: Assuming that program memory still contains the last program from the preceding section (which consisted of 17 program lines), store after that program the office-supplies program from Section 8 (page 86). Since this is the second program to be stored in program memory, we’ll ensure that a i000 instruction separates it from the first program by doing step 3 in the procedure above.
Section 11: Multiple Programs Keystrokes Display (RPN mode) Sets calculator to Program mode. 000, gi.027 027,43,33,019 Sets calculator to last line keyed into program memory. 028, 029, 030, Keys in program 031, 032, 033, gi029 034,43,33,029 Running Another Program To run a program that does not begin with program line 001: 1.
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 Example 1: A borrower is charged 2 points for the issuance of his mortgage. If the mortgage amount is $60,000 for 30 years and the interest rate is 11½% per year, with monthly payments, what true annual percentage rate is the borrower paying? (One point is equal to 1% of the mortgage amount.) Keystrokes (RPN mode) Display...
Section 12: Real Estate and Lending Example 3: Again using the information given in example 1, what is the APR if the mortgage fee is stated as 2 points plus $150? Keystrokes (RPN mode) Display gÂ fCLEARG 30gA Months (into n) 360.00 11.5gC Percent monthly interest rate (into...
Section 12: Real Estate and Lending Example 1: A lender wishes to induce the borrower to prepay a low interest rate loan. The interest rate is 5% with 72 payments remaining of $137.17 and a balloon payment at the end of the sixth year of $2000. If the lender is willing to discount the future payments at 9%, how much would the borrower need to prepay the note? Keystrokes (RPN mode)
Section 12: Real Estate and Lending payment, as well as the number of payment periods per year, the price paid for the mortgage, and the balloon payment amount (if it exists). Information is entered as follows: 1. Press gÂ and fCLEARG. 2.
Section 12: Real Estate and Lending Example 2: Using the same information given in example 1, calculate the annual yield if the loan is to be paid in full at the end of the fifth year (from original issuance). (In this case both the payment amount and the balloon must be calculated since they are not given.) Keystrokes (RPN mode) Display...
Section 12: Real Estate and Lending KEYSTROKES KEYSTROKES DISPLAY DISPLAY (RPN mode) (RPN mode) Þ 023, 057, 024, 058, § ¼ 025, 059, 026, 060, 45,43 027, 061, 028, 062, 029, 063, 030, 064, 031, FV is repeated in the program twice to ensure that it is computed and not stored. REGISTERS n: Period i: Apprec.
Section 12: Real Estate and Lending 9. Key in the monthly rent for the alternative housing then press ?8. 10. Key in the savings or alternative investment annual interest rate as a percentage then press ?9. 11. Key in the combined State and Federal marginal tax rate as a percentage then press ?.0.
Section 12: Real Estate and Lending An alternative would be to rent a similar dwelling at $400 per month and to invest the difference between the purchase cost and rent at 6¼% interest. Your personal income tax rate (marginal) is 25% Federal and 5% State. Which alternative is more financially attractive? Keystrokes (RPN mode) Display...
Section 12: Real Estate and Lending Keystrokes Display fCLEARH Initialize. 0.00 First cash flow. 0.00 Second through ninth cash flows. 0.00 8.00 7000gK Tenth through thirteenth cash flows. 7,000.00 4.00 6¼ Interest. 6.00 15,218.35 NPV. 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.
Section 12: Real Estate and Lending Keystrokes Display fCLEARH Initialize. 0.00 500gJ First cash flow. 500.00 Second thru sixth cash flows. 500.00 5.00 600gK Next twelve cash flows. 600.00 12ga 12.00 750gK Last six cash flows. 750.00 6.00 13.5gC Monthly interest rate 1.13 12,831.75 Amount to invest to achieve a 13.5% yield.
Straight-Line Depreciation The following HP 12C Platinum program (written in RPN mode) calculates the straight-line depreciation for the year desired with the acquisition date occurring at any time during the year.
Section 13: Investment Analysis 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. s t y e a r 3 r d y e a r 2 n d y e a r...
4.5t First year: 1.00 depreciation. 504.75 Declining-Balance Depreciation The following HP 12C Platinum program (written in RPN mode) calculates the declining-balance depreciation for the year desired with the acquisition date occurring at any time during the year. KEYSTROKES KEYSTROKES DISPLAY...
2.00 Second year: 2.00 depreciation. 11,458.33 Sum-of-the-Years-Digits Depreciation The following HP 12C Platinum program (written in RPN mode) calculates the sum-of-the-years-digits depreciation for the year desired with the acquisition date occurring at any time during the year. KEYSTROKES KEYSTROKES DISPLAY...
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 Platinum program calculates the optimum crossover point and automatically switches to straight-line depreciation at the appropriate time.
Section 13: Investment Analysis 7. Key in the desired year and press \. 8. Key in the number of months in the first year then press t calculate the amount of depreciation for the desired year. 9. If desired, press ~ to see the remaining depreciable value. 10.
Section 13: Investment Analysis Keystrokes (RPN mode) Display Sixth year: 6.00 depreciation. 761.35 Seventh year: 7.00 depreciation. 713.62 Total depreciation through the 9,429.56 seventh year. Eight year: 8.00 depreciation 713.63 Ninth year: 9.00 depreciation. 356.81 a By observation the crossover was year 6. Years 7, 8, and 9 use straight-line depreciation.
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.
Section 13: Investment Analysis This Modified Internal Rate of Return procedure (MIRR) is one of several IRR alternatives which avoids the drawbacks of the traditional IRR technique. The procedure eliminates the sign change problem and the reinvestment (or discounting) assumption by utilizing user stipulated reinvestment and borrowing rates.
Section 14: Leasing Section 14 Leasing Advance Payments Situations may exist where payments are made in advance (leasing is a good example). These agreements call for extra payments to be made when the transaction is closed. This first procedure finds the periodic payment amount necessary to achieve a desired yield when a number of payments are made in advance.
Section 14: Leasing If solving for the payment amount will be done repetitively, key in the following HP 12C Platinum program. KEYSTROKES KEYSTROKES DISPLAY DISPLAY (RPN mode) (RPN mode) 009, Þ 000, 010, 000, 011, CLEAR Î gÂ 001, 012,...
Section 14: Leasing Example 2: Using the preceding program, solve for the monthly payment using the information given in example 1. Then change the yearly interest to 15% and solve for the new payment amount. Keystrokes (RPN mode) Display 12?0 Duration of lease.
:P§+$ -23,200.00 PV. ¼ Monthly yield (calculated). 1.44 12§ Annual yield (as a percentage). 17.33 If solving for yield will be done repetitively, key in the following HP 12C Platinum program: KEYSTROKES KEYSTROKES DISPLAY DISPLAY (RPN mode) (RPN mode) 009, Þ...
Section 14: Leasing REGISTERS n: n–#Adv. i: i PV: Used PMT: Pmt. Pmts. FV: 0 : Adv. Pmts. : Pmt. : Loan : Unused – 1. Key in the program. 2. Key in the total number of payments in the lease then press ?0. 3.
Section 14: Leasing Example 1: A copier worth $22,000 is to be leased for 48 months. The lessee has agreed to make 4 payments in advance, with a purchase option at the end of 48 months enabling him to buy the copier for 30% of the purchase price. What monthly payment is necessary to yield the lessor 15% annually: Keystrokes (RPN mode) Display...
4. Key in 0gK then the number of advance payments minus one. Then press ga. 5. Key in the residual then press gK. Then press fL to solve for periodic yield. Example: Equipment worth $5000 is leased for 36 months at $145 per month. The lessee has agreed to pay the first and last month’s payments in advance.
Keystrokes (RPN mode) Display M¼ 1.31 :n§ Percent nominal interest rate. 5.25 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.
Section 16: Bonds Section 16 Bonds 30/360 Day Basis Bonds A bond is a contract to pay interest, usually semiannually, at a given rate (coupon) and to pay the principal of the bond at some specified future date. A bond which is calculated on a 30/360 day basis is one in which the day count basis is computed using 30 days in a month and 360 days in a year.
8.00 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/...
Section 16: Bonds For annual coupon bonds calculated on a 30/360 day basis, insert d after gÒ at steps 19 and 23 (making the program two steps longer). 1. Key in the program and press ?Æ if the C status indicator is not displayed.
Appendix A RPN and the Stack In RPN mode, four special registers in the HP 12C Plati- num 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 rea- son, they are generally referred to as the “stack registers”...
That’s basically how the stack operates. In the rest of this appendix, we’ll take a more detailed look at how numbers are entered into and rearranged within the stack, and the effect of the various HP 12C Platinum functions on the numbers in the stack.
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 –...
Appendix A: RPN and the Stack Pressing d four times successively displays the numbers in the Y-, Z-, and T-registers and returns the numbers to their original registers. One-Number Functions and the Stack One-number mathematics and number-alteration functions – y, r, ¿ >, ’, e, B, Ñ, and T –...
Appendix A: RPN and the Stack ddition Subtraction Multiplication Division When an arithmetic operation or q is performed, the answer is placed in the X-register, the number formerly in the X-register is copied into the LAST X reg- ister, 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.
Appendix A: RPN and the Stack Calendar and Financial Functions The following table shows what quantity is in each stack register after the indi- cated calendar or financial function key is pressed. The symbols x, y, z, and t rep- resent 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 The number in the displayed X-register is copied into the LAST X register when- ever any of the following function keys is pressed: § > ¿ Ñ à Ò...
Appendix A: RPN and the Stack The diagram on page 167 illustrates how the automatic stack lift and stack drop make chain calculations quick and error-free. Virtually every chain calculation you are likely to encounter can be done using only the four stack registers. However, to avoid having to store an intermediate result in a storage register, you should begin every chain calculation at the inner- most number or pair of parentheses and then work outward –...
Appendix A: RPN and the Stack Keystrokes (RPN mode) Display Enters constant into Y-, Z-, and 2.00 T-registers. 84000 Enters base amount into displayed 84,000. X-register. § 168,000.00 Annual sales after first year. § 336,000.00 Annual sales after second year. §...
Appendix B Algebraic Mode (ALG) To select algebraic mode, press f[. When the calculator is in algebraic mode, the ALG status indicator is lit. Simple Arithmetic calculations in ALG mode To calculate 21.1 + 23.8: Keystrokes (ALG mode) Display 21.1+ 21.10 23.8 23.80...
Appendix B: Algebraic Mode (ALG) Chain Calculations in ALG mode To do a chain calculation, you don’t need to press } after each operation, but only at the very end. × 750 12 For instance, to calculate you can enter either: -------------------- - 750 §...
Appendix B: Algebraic Mode (ALG) Percent Difference To find the percent difference between two numbers: 1. Key in the base number. 2. Press } to separate the other number from the base number. 3. Key in the other number. 4. Press à. Example: Yesterday your stock fell from 35.5 to 31.25 per share.
Appendix B: Algebraic Mode (ALG) The Power Function Pressing q calculates a power of a number, that is, y . Like the arithmetic function +, q requires two numbers: 1. Key in the base number (which is designated by the y on the key). 2.
IRR answer exists, and what that answer is. For the vast majority of cases, your HP 12C Platinum will find the unique IRR answer if it exists. But the IRR computation is so complex that if the cash flow sequence does not meet certain criteria, then sometimes the calculator is unable to determine whether or not an answer or answers exist.
Appendix C: More About L Your guess will aid the calculator in its search, and if it finds an IRR answer near your guess, that answer will be displayed. Since the calculator cannot tell you the number of solutions that exist when there is more than one mathematically cor- rect answer, you can continue to make guesses, pressing :gt after each one, to search for IRR solutions.
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 condi- tions, 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 spec- ified.
Appendix D: Error Conditions Error 8: Calendar Operation Condition Ò Improper date format or illegal date. Attempting to add days beyond calcula- tor’s date capacity. Improper date format or illegal date. More than 500 years between settlement (purchase) date and maturity (redemption) date.
Formulas Used Percentage Base y ( ) Rate x ( ) × ---------------------------------------------- NewAmount x ( ) Base y ( ) – ∆% = ------------------------------------------------------------------- - Base y ( ) Amount x ( ) %T = ---------------------------- - ...
Appendix : Formulas Used INTG n ( ) – – iFRAC n ( ) )PMT PV 1 --------------------------------------------- - INTG n ( ) – FV 1 With compound interest used for an odd period: INTG n ( ) – – FRAC n ( ) )PMT PV 1...
Appendix : Formulas Used = cash flow at period j. … NPV = ----------------- - ----------------- - ----------------- - Internal Rate of Return = number of cash flows = cash flow at period j. = Internal Rate of Return ∑ –...
Appendix : Formulas Used Sum-of-the-Years-Digits Depreciation SOYD ------------------------------------------ where W = integer part of k F = fractional part of k. (i.e., for k = 12.25 years, W = 12 and F = 0.25). Keyboard function: L j – ⋅ ------------------------ - SBV SAL –...
Appendix : Formulas Used -- - MIRR = -------------- - – Advance Payments = number of payments made in advance. n – PV FV 1 – PMT = -------------------------------------------------------- - – – – ---------------------------------------- - Interest Rate Conversions = number of compounding periods per year.
Appendix : Formulas Used Weighted Mean ∑ ------------- - ∑ Linear Estimation n = number of data pairs y ˆ – x ˆ ----------- - ∑ ∑ ⋅ ∑ – ----------------------- - where B = ------------------------------------------ - ∑ ∑ – ---------------- - y Bx –...
Appendix : Formulas Used ∏ n! = The Rent or Buy Decision Market Value = PRICE(1 + I) where: = appreciation per year (as decimal) = number of years Net Cash Proceeds on Resale = Market Value – Mortgage Balance – Commis- sion The interest rate is obtained by solving the financial (compound interest) equa- tion for i using:...
Information Battery The HP 12C Platinum is shipped with one 3 Volt CR2023 Lithium battery. Bat- tery 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.
Appendix F: Battery, Warranty, and Service Information To install a new battery, use the following procedure: 1. With the calculator turned off, slide the battery cover off. 2. Remove the old battery. 3. Insert a new battery, with positive polarity facing outward. 4.
The status indicators turned on at the end of this test include some that normally are not displayed on the 12C Platinum. If the calculator displays Error 9 as a result of the ;/§ test or the ;/+ test but you wish to continue using your calculator, you should reset Continuous Memory as described on page 70.
Replacement products may be either new or like-new. 2. HP warrants to you that HP software will not fail to execute its programming instructions after the date of purchase, for the period specified above, due to defects in material and workmanship when properly installed and used.
8. The only warranties for HP products and services are set forth in the express warranty statements accompanying such products and services .
Appendix F: Battery, Warranty, and Service Information Service Europe Country : Telephone numbers Austria +43-1-3602771203 Belgium +32-2-7126219 Denmark +45-8-2332844 Eastern Europe +420-5-41422523 countries Finland +35-89640009 France +33-1-49939006 Germany +49-69-95307103 Greece +420-5-41422523 Holland +31-2-06545301 Italy +39-0422-303069 Norway +47-63849309 Portugal +351-213-180020 Spain +34-917-820111 Sweden +46-851992065...
However, there is no guarantee that interference will not occur in a particular installation. If your HP 12C Platinum does cause inter- ference to radio or television reception, which can be determined by turning the...
Appendix F: Battery, Warranty, and Service Information calculator off and on, you are encouraged to try to correct the interference by one or more of the following measures: Reorient the receiving antenna. Relocate the calculator with respect to the receiver. Move the calculator away from the receiver.
Appendix G United Kingdom Calculations The calculations for most financial problems in the United Kingdom are identi- cal to the calculations for those problems in the United States – which are described earlier in this handbook. Certain problems, however, require different calculation methods in the United Kingdom than in the United States, even though the terminology describing the problems may be similar.
Appendix G: United Kingdom Calculations Bond Calculations Solutions for the price and yield to maturity of United Kingdom bonds are not included in this handbook. Actual practice differs according to the type of bond; variations such as cumulative and ex-dividend pricing, simple or compound interest discounting, etc., may be encountered.
Function Key Index General . Decimal point (page Percentage 17). Also used for dis- b Computes x% of y and ; Power on /off key play formatting (page retains the y-value in the (page 16). 72). Y-register (page 27). f Shift key. Selects alter- OClears contents of à...
Function Key Index Â Sets payment l Calculates the net a Stores the number mode to End for com- present value of up to (from 1 to 99) of times pound interest calcula- 30 uneven cash flows each cash flow occurs tions involving and initial investment as N...
Function Key Index R Linear estimate Mathematics Number Alteration (X-register), correlation r Computes square root B Rounds mantissa of coefficient (Y-register). of number in displayed 10-digit number in X-regis- Fits a line to a set of (x,y) X-register (page 82). ter to match the display data pairs entered using (page 82).
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).
Programming Key Index Program Mode Run Mode Active Keys: Pressed from Executed as a recorded keyboard: program instruction: t Run/Stop. Begins t Run/Stop. Stops execution of a stored program execution program. Stops execu- (page 98). tion if program is run- ning (page 87).
Index Bonds, state and local government 67 Bonds, U.S. Treasury 67 – Branching 101 – Branching, adding instructions by 113 – Branching, conditional 104 Branching,simple 101 Ü Buying versus Renting 127 C status indicator 53 – – Calendar functions 30 Calendar functions and the stack 171 –...
Index – D.MY status indicator 31 – Data storage registers 23 Date format 30 Dates, days between 32 Dates, future or past 31 Days, between dates 32 Decimal places, rounding 71 Decimal point, changing 17 Declining-balance depreciation 137 – Deferred annuities 131 –...
Index Errors, in digit entry 75 Excess depreciation 145 Æ Exponent 18 Exponential 82 Factorial 82 Financial registers 34 Financial registers, clearing 34 Fractional 83 Future value 38 Future value, calculating 49 FV 38 G–K Indicators, status 70 Instructions in program lines 89 ¼...
Index Low-power indicator 16 Mantissa 18 Mantissa Display Format 73 Mean 77 Ö Mean, weighted 81 memory 23 Memory, program 91 Modes alegebraic 19 RPN 19 Modified internal rate of return 145 Mortgage, price of 124 Mortgage, yield of 125 Multiple programs 117 Negative numbers 17 Net amount 27...
Index One-variable statistics 76 Overflow 73 Partial-year depreciation 134 Payment 38 Payment amount, calculating 48 Payment mode 38 Payments, advance 148 Payments, number of 41 Percent difference 28 Percent of total 29 Percentages 27 PMT 38 Populations 79 Power function 84 Pr error 74 Prefix key 16 Present value 38...