58.33 58.33 22.95 35.38

Keys the first number. Pressing \ separates the second number from the first. Keys in the second number. Pressing - subtracts the second number from the first. The calculator displays the result of this calculation, which is the balance after subtracting the first check. Keys in the next number. Since a calculation has just been performed, do not press \; the next number entered (13.70) is automatically separated from the one previously in the display (35.38).
Page: 20 of 209 Dimension: 14.8 cm x 21 cm

Keystrokes -

Display
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. Keys in the next number and subtracts it from the previous balance. The new balance appears in the display. (Its getting rather low!) Keys in the next number the paycheck deposited and adds it to the previous balance. The new, current balance appears in the display.

10.14-

1,064.54
The preceding example demonstrates how the hp 12c calculates just as you would using pencil and paper (except a lot faster!):
Lets see this happening in a different type of calculation one that involves multiplying groups of two numbers and then adding the results. (This is the type of calculation that would be required to total up an invoice consisting of several items with different quantities and different prices.) For example, consider the calculation of (3 4) + (5 6). If you were doing this on paper, you would first do the multiplication in the first parentheses, then the multiplication in the second parentheses, and finally add the results of the two multiplications:
Page: 21 of 209 Dimension: 14.8 cm x 21 cm
Your hp 12c calculates the answer in just the same way: Keystrokes 3\4 5\6 + Display

12.00 30.00 42.00

Step 1: Multiply the numbers in the first parentheses. Step 2: Multiply the numbers in the second parentheses. 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. And after you keyed in the 5 and the 6 in step 2, the calculator was holding two numbers (12 and 5) inside for you, in addition to the 6 in the display. (The hp 12c can hold a total of three numbers inside, in addition to the number in the display.) After step 2, the calculator was still holding the 12 inside for you, in addition to the 30 in the display. You can see that the calculator holds the number for you, just as you would have them written on paper, and then calculates with them at the proper time, just as you would yourself.* But with the hp 12c, you dont need to write down the results of an intermediate calculation, and you dont even need to manually store it and recall it later. By the way, notice that in step 2 you needed to press \ again. This is simply because you were again keying in two numbers immediately following each other, without performing a calculation in between. To check your understanding of how to calculate with your hp 12c, try the following problems yourself. Although these problems are relatively simple, more complicated problems can be solved using the same basic steps. If you have difficulty obtaining the answers shown, review the last few pages.

The Cash Flow Sign Convention
When entering the PV, PMT, and FV cash flows, the quantities must be keyed into the calculator with the proper sign, + (plus) or (minus), in accordance with The Cash Flow Sign Convention: Money received (arrow pointing up) is entered or displayed as a positive value (+). Money paid out (arrow pointing down) is entered or displayed as a negative value ().
Page: 36 of 209 Dimension: 14.8 cm x 21 cm

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. 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.
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. To specify the payment mode: Press g if payments are made at the beginning of the compounding periods. Press g if payments are made at the end of the compounding periods. The BEGIN status indicator is lit when the payment mode is set to Begin. If BEGIN is not lit, the payment mode is set to End. The payment mode remains set to what you last specified until you change it; it is not reset each time the calculator is turned on. However, if Continuous Memory is reset, the payment mode will be set to End.
Generalized Cash Flow Diagrams
Examples of various kinds of financial calculations, together with the applicable cash flow diagrams, appear under Compound Interest Calculations later in this section. If your particular problem does not match any of those shown, you can solve it nevertheless by first drawing a cash flow diagram, then keying the quantities identified in the diagram into the corresponding registers. Remember always to observe the sign convention when keying in PV, PMT, and FV. The terminology used for describing financial problems varies among the different segments of the business and financial communities. Nevertheless, most problems involving compound interest can be solved by drawing a cash flow diagram in one of the following basic forms. Listed below each form are some of the problems to which that diagram applies.

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. You open the account with a deposit of $3,200 and intend to make semiannual deposits, beginning six months later, from your profit-sharing bonus paychecks. Calculate how much these deposits should be.
Keystrokes fCLEARG 15\2w 9.75\2z 3200$ 60000M g P

30.00 4.88 3200.00

Calculates and stores n. Calculates and stores i. Stores PV (with minus sign for cash paid out).
60,000.00 Stores FV. 60,000.00 Sets payment mode to End. 717.44
Semiannual payment (with minus sign for cash paid out).
Page: 47 of 209 Dimension: 14.8 cm x 21 cm
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 or C. 4. Enter either or both of the following: Present value, using $. 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. Example 1: In Example 1 on page 46, we calculated that the payment amount on a 29-year, $43,400 mortgage at 141/4% annual interest is $523.99. If the seller requests a balloon payment at the end of 5 years, what would be the amount of the balloon?
Keystrokes fCLEARG 5gA 14.25gC 43400$ 523.99P g M

60.00 1.19 523.99 523.99

Calculates and stores n. Calculates and stores i. Stores PMT (with minus sign for cash paid out). Sets payment mode to End.

43,400.00 Stores PV.

42,652.37 Amount of balloon payment.
Page: 48 of 209 Dimension: 14.8 cm x 21 cm
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 fCLEARG 2gA 6.25gC 50P g M
24.00 0.52 50.00 50.00 1,281.34
Calculates and stores n. Calculates and stores i. Stores PMT (with minus sign for cash paid out). Sets payment mode to Begin. Balance after 2 years.
Example 3: Property values in an unattractive area are depreciating at the rate of 2% per year. Assuming this trend continues, calculate the value in 6 years of property presently appraised at $32,000.

Keystrokes fCLEARG 6n

Stores n.
Page: 49 of 209 Dimension: 14.8 cm x 21 cm

Keystrokes $ M

2.00 32,000.00 28,346.96
Stores i (with minus sign for a negative interest rate). Stores PV (with minus sign for cash paid out). Property value after 6 years.

you have stored a program in the calculator, the number of registers available for storing
cash flow amounts may be less than 21. (Storage registers are automatically allocated to program lines beginning with R.9 and proceeding in reverse order to R7, as described on pages 93 thru 95.) The maximum number of cash flow amounts (in addition to CF0) that can be stored is the number that appears at the right of the display when gN is pressed. If the maximum number of cash flow amounts is stored, the final cash flow amount is always stored in the FV register. For example, if N displays P-08 r-20, the last cash flow amount that can be stored CF20 will be stored in FV. Similarly, if N displays P-22 r-18, the last cash flow amount that can be stored CF18 will be stored in FV.
Page: 59 of 209 Dimension: 14.8 cm x 21 cm
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. Therefore, these cash flows must be entered using the method described above. Keystrokes fCLEARH 80000gJ 500gK 4500gK 5500gK 4500gK 130000gK :n 13 fl Display
Clears financial and storage registers. negative cash flow).
80,000.00 Stores CF0 (with minus sign for a 500.00 4,500.00 5,500.00 4,500.00
Stores CF1 (with minus sign for a negative cash flow). Stores CF2. Stores CF3. Stores CF4.
130,000.00 Stores CF5. 5.00 13.00 212.18
Checks number of cash flow amounts entered (in addition to CF0 ). Stores i. NPV.
Since NPV is positive, the investment would increase the financial value of the investors assets.
Page: 60 of 209 Dimension: 14.8 cm x 21 cm
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. This number is designated Nj, corresponding to cash flow amount CFj, and is entered using the a key. Each Nj is stored in a special register inside the calculator. This method can, of course, be used for problems involving fewer than 20 cash flows and it will require fewer storage registers than the method described above under Calculating NPV for Ungrouped Cash Flows. Equal consecutive cash flows can be entered using that method provided there are enough storage registers available to accommodate the total number of individual cash flows. The facility of grouping equal consecutive cash flows is provided to minimize the number of storage registers required. Note: When entering cash flow amounts including the initial investment CF0 remember to observe the cash flow sign convention by pressing after keying in the amount for a negative cash flow. In summary, to enter the amounts of the cash flows and the number of times they occur consecutively: 1. Press fCLEARH to clear the financial and storage registers. 2. Key in the amount of the initial investment, press if that cash flow is negative, then press gJ. If there is no initial investment, press 0gJ. 3. If the initial investment consists of more than one cash flow of the amount entered in step 2, key in the number of those cash flows, then press ga. If ga is not pressed, the calculator assumes that N0 is 1. 4. Key in the amount of the next cash flow, press if that cash flow is negative, then press gK. If the cash flow amount is zero in the next period, press 0gK. 5. If the amount entered in step 4 occurs more than once consecutively, key in the number of times that cash flow amount occurs consecutively, then press ga. If ga is not pressed, the calculator assumes that Nj is 1 for the CFj just entered. 6. Repeat steps 4 and 5 for each CFj and Nj until all cash flows have been entered. With the amounts of the cash flows and the number of times they occur consecutively stored in the calculator, NPV can be calculated by entering the interest rate and pressing fl, just as described earlier.

1.00 100,000.00 1.00 4,500.00 2.00 9,000.00
N7 CF7 N6 CF6 N5 CF5. N1 CF1 N0 CF0 Resets the number in the n register to its original value.
1.00 14,000.00 1.00 79,000.00 7.00
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. To change the number of times a cash flow amount occurs consecutively that is, to change the Nj for a CFj: 1. Store the number of that cash flow amount (that is, j) in the n register. 2. Key the number of times the cash flow amount occurs consecutively into the display. 3. Press ga.
Page: 65 of 209 Dimension: 14.8 cm x 21 cm
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. Keystrokes 9000?2 13.5 fl Display

9,000.00 13.50 644.75

Stores the new CF2 in R2. Stores i.* The new NPV.
Since this NPV is negative, the investment would decrease the financial value of the investors assets. Example 2: Change N5 from 2 to 4, then calculate the new NPV. Keystrokes 5n 4ga 7n fl Display

5.00 4.00 7.00 1,857.21

Stores j in the n register. Stores the new N5. Resets the number in the n register to its original value. The new NPV.

Bond Calculations

The hp 12c 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. Treasury bonds and U.S. Treasury notes). In accordance with market convention, prices are based on a redemption (par) value of 100.
* This step is necessary in this example because we have calculated IRR since the first time we
calculated NPV. The IRR calculation replaced the 13.5 we keyed into i before calculating NPV with the result for IRR 13.72.
All bond calculations are performed in accordance with. the Securities Industry Associations

recommendations as contained in Spence, Graudenz, and Lynch, Standard Securities Calculation Methods, Securities Industry Association, New York, 1973.
Page: 66 of 209 Dimension: 14.8 cm x 21 cm
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. 2. Enter the annual coupon rate (as a percentage), using P. 3. Key in the settlement (purchase) date (as described on page 29), then press \. 4. Key in the maturity (redemption) date. 5. Press fE. The price is shown in the display and also is stored in the PV register. The interest accrued since the last interest date is held inside the calculator: to display the interest, press ~; to add the interest to the price, press +. Example: What price should you pay on April 28, 2004 for a 63/4% U.S. Treasury bond that matures on June 4, 2018, if you want a yield of 81/4%. Assume that you normally express dates in the month-day-year format. Keystrokes 8.25 6.75P g 4.282004\ 6.042018 fE + Display
8.25 6.75 6.75 4.28 6.042018 87.62 90.31
Enters yield to maturity. Enters coupon rate. Sets date format to month-day-year. Enters settlement (purchase) date. Enters maturity (redemption) date. Bond price (as a percent of par). Total price, including accrued interest.

Bond Yield

1. Enter the quoted price (as a percent of par), using $. 2. Enter the annual coupon rate (as a percentage), using P. 3. Key in the settlement (purchase) date, then press \. 4. Key in the maturity (redemption) date. 5. Press fS. The yield to maturity is shown in the display and also is stored in the i register. Note: Remember that the S function may take a significant amount of time to produce an answer, during which the calculator displays running.
Page: 67 of 209 Dimension: 14.8 cm x 21 cm
Example: The market is quoting 883/8% for the bond described in the preceding example. What yield will that provide? Keystrokes 3\8z 88+$ 6.75P 4.282004\ 6.042018 fS Display
0.38 88.38 6.75 4.28 6.042018 8.15
Calculates 3/8. Enters quoted price. Enters coupon rate. Enters settlement (purchase) date. Enters maturity (redemption) date. Bond yield.
Depreciation Calculations
The hp 12c enables you to calculate depreciation and the remaining depreciable value (book value minus salvage value) using the straight-line, sum-of-the-years-digits, and declining-balance methods. To do so with any of these methods: 1. Enter the original cost of the asset, using $. 2. Enter the salvage value of the asset, using M. If the salvage value is zero, press 0M. 3. Enter the expected useful life of the asset (in years), using n. 4. If the declining-balance method is being used, enter the declining-balance 1 factor (as a percentage), using. For example, 1 /4 times the straight-line rate 125 percent declining-balance would be entered as 125. 5. Key in the number of the year for which depreciation is to be calculated. 6. Press: fV for depreciation using the straight-line method. f for depreciation using the sum-of-the-years digits method. f# for depreciation using the declining-balance method. V, , 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 ~.

The reliability of a linear estimate depends upon how closely the data pairs would, if plotted on a graph, lie in a straight line. The usual measure of this reliability is
the correlation coefficient, r. This quantity is automatically calculated whenever y or x is calculated; to display it, press ~. A correlation coefficient close to 1 or 1 indicates that the data pairs lie very close to a straight line. On the other hand, a correlation coefficient close to 0 indicates that the data pairs do not lie closely to a straight line; and a linear estimate using this data would not be very reliable.
Example: Check the reliability of the linear estimate in the preceding example by displaying the correlation coefficient. Keystrokes ~ Display
The correlation coefficient is close to 1, so the sales calculated in the preceding example is a good estimate.
To graph the regression line, calculate the coefficients of the linear equation y = A + Bx. 1. Press 0gR to compute the y-intercept (A). 2. Press 1gR~d~- to compute the slope of the line (B).
Page: 80 of 209 Dimension: 14.8 cm x 21 cm
Example: Compute the slope and intercept of the regression line in the preceding example. Keystrokes 0gR 1 gR~d~Display

15.55 0.001

y-intercept (A); projected value for x = 0. 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 + 0.001x

Weighted Mean

You can compute the weighted mean of a set of numbers if you know the corresponding weights of the items in question. 1. Press fCLEAR. 2. Key in the value of the item and press \, then key in its weight and press _. Key in the second items value, press \, key in the second weight, and press _. Continue until you have entered all the values of the items and their corresponding weights. The rule for entering the data is item \ weight _. 3. Press g to calculate the weighted mean of the items. Example: Suppose that you stop during a vacation drive to purchase gasoline at four stations as follows: 15 gallons at $1.16 per gallon, 7 gallons at $1.24 per gallon, 10 gallons at $1.20 per gallon, and 17 gallons at $1.18 per gallon. You want to find the average cost per gallon of gasoline purchased. If you purchased the same quantity at each station, you could determine the simple arithmetic average or mean using the key. But since you know the value of the item (gasoline) and its corresponding weight (number of gallons purchased), use the key to find the weighted mean: Keystrokes fCLEAR 1.16\15_ 1.24\7_ 1.20\10_ 1.18\17_ Display

Page: 95 of 209 Dimension: 14.8 cm x 21 cm
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. For example, assuming the calculator is still in Program mode, you can set it to program line 00 as follows: Keystrokes gi.00 Display

Program line 00

Executing a Program One Line at a Time
Pressing repeatedly with the calculator in Program mode (as described earlier) enables you to verify that the program you have stored is identical to the program you wrote that is, to verify that you have keyed the instructions in correctly. However, this does not ensure that the program you wrote calculates the desired results correctly: even programs created by the most experienced programmers often do not work correctly when they are first written. To help you verify that your program works correctly, you can execute the program one line at a time, using the key. Pressing while the calculator is in Run mode advances the calculator to the next line in program memory, then displays that lines number and the keycode of the instruction stored there, just as in Program mode. In Run mode, however, when the key is released the instruction in the program line just displayed is executed and the display then shows the result of executing that line. For example, to execute the program stored in the calculator one line at a time: Keystrokes fs Display

124.25

Sets calculator to Run mode and to line 00 in program memory. (Display shown assumes results remain from previous calculation.) Keys in price of typewriter.

625. 01625.00

36 Program line 01: \
Result of executing program line 01.

2 Program line 02: 2.

Page: 96 of 209 Dimension: 14.8 cm x 21 cm

Keystrokes

Result of executing program line 02.

5 Program line 03: 5.

Result of executing program line 03.

04156.25

0000010203- 44 04050607- 44 0809- 44 0.00 68.5 890.50 60.11 950.61 72.9 1,312.20 88.57 1,400.6,370.20
31 Stops program execution to display

AMOUNT.

Stops program execution to display
Sets calculator to Run mode. Clears registers R1 through R6. First item. AMOUNT for first item. TAX for first item. TOTAL for first item. Second item. AMOUNT for second item. TAX for second item. TOTAL for second item.
Page: 101 of 209 Dimension: 14.8 cm x 21 cm
102 Section 8: Programming Basics
Keystrokes 24\85 t t t 5\345 t t t :1 :2 :3
85. 2,040.00 137.70 2,177.70 345. 1,725.00 116.44 1,841.44 5,967.70 402.82 6,370.52
Third item. AMOUNT for third item. TAX for third item. TOTAL for third item. Fourth item. AMOUNT for fourth item. TAX for fourth item. TOTAL for fourth item. Sum of AMOUNT column. Sum of TAX column. Sum of TOTAL column.
Program execution is also automatically halted when the calculator overflows (refer to 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. To determine at which program line execution has halted (in order to locate the error), press any key to clear the Error display, then press fs to set the calculator to Program mode and display that program line. You may also want to display the current program line (by pressing fs) if your program has halted at one of several t instructions in your program and you want to determine which one that is. To continue executing the program afterward: 1. Press fs to set the calculator back to Run mode. 2. If you want to resume execution from the program line at which execution halted rather than from line 00, press gi followed by two digit keys that specify the program line desired. 3. Press t to resume execution. Stopping Program Execution Manually. Pressing any key while a program is running halts program execution. You may want to do this if the calculated results displayed by a running program appear to be incorrect (indicating that the program itself is incorrect). To halt program execution during a pause in a running program (that is, when u is executed), press any key. After stopping program execution manually, you can determine at which program line execution has halted and/or resume program execution as described above.
Page: 102 of 209 Dimension: 14.8 cm x 21 cm

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.

Page: 148 of 209 Dimension: 14.8 cm x 21 cm
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. The figure generally used is a short-term security (T-Bill) or bank passbook rate. Positive cash flows are reinvested at a reinvestment rate which reflects the return on an investment of comparable risk. An average return rate on recent market investments might be used. The steps in the procedure are: 1. Calculate the future value of the positive cash flows (NFV) at the reinvestment rate. 2. Calculate the present value of the negative cash flows (NPV) at the safe rate. 3. Knowing n, PV, and FV, solve for i. Example: An investor has the following unconventional investment opportunity. The cash flows are:

# of Months

Cash Flow ($)
180,000 100,000 100,200,000
Calculate the MIRR using a safe rate of 6% and a reinvestment (risk) rate of 10%. Keystrokes fCLEARH 0gJ 100000gK 5ga 0gK5ga 0gK9ga 200000gK Display
0.00 0.00 5.00 5.00 9.00 200,000.00
First cash flow. Second through sixth cash flows. Next five cash flows. Next nine cash flows. Last cash flow.
Page: 149 of 209 Dimension: 14.8 cm x 21 cm
150 Section 13: Investment Analysis
Keystrokes 10gCfl $ 20nM 180000gJ 0gK5ga 100000K 5ga 6gCfl 20n 12

657,152.37 775,797.83

NPV of positive cash flows. NFV of positive cash flows.

-660,454.55 0.81 9.70

NPV of negative cash flows. Monthly MIRR Annual MIRR.
Page: 150 of 209 Dimension: 14.8 cm x 21 cm

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.

Solving For Payment

To calculate the payment, 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 or calculate the periodic interest rate as a percentage then press. 5. Press 1$:0+. 6. Key in the initial loan amount then press ~z, to obtain the periodic payment to be received by the lessor. Example 1: Equipment worth $750 is leased for 12 months. The equipment is assumed to have no salvage value at the end of the lease. The lessee has agreed to make three payments at the time of closing. What monthly payment is necessary to yield the lessor 10% annually? Keystrokes g fCLEARG 12\ 3?0-n 10gC 1P $:0+ 750~z Display

incorrectly replaced. Replace only with the same or equivalent type recommended by the manufacturer. Dispose of used batteries according to the manufacturers instructions. Do not mutilate, puncture, or dispose of batteries in fire. The batteries can burst or explode, releasing hazardous chemicals. Replacement battery is a Lithium 3V Coin Type CR2032.

Installing a New Battery

The contents of the calculators Continuous Memory are preserved for a short time while the battery is out of the calculator (provided that you turn off the calculator before removing the battery). This allows you ample time to replace the battery without losing data or programs. If the battery is left out of the calculator for an extended period, the contents of Continuous Memory may be lost.
Page: 193 of 209 Dimension: 14.8 cm x 21 cm
194 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. If you do so, the contents of Continuous Memory may be lost and keyboard control may be lost (that is, the calculator may not respond to keystrokes). 5. Replace the battery compartment cover and press ; to turn on the power. If for any reason Continuous Memory has been reset (that is, if its contents have been lost), the display will show Pr Error. Pressing any key will clear this message.
Verifying Proper Operation (Self-Tests)
If it appears that the calculator will not turn on or otherwise is not operating properly, use one of the following procedures. For a calculator that does respond to keystrokes: 1. With the calculator off, hold down the ; key and press. 2. Release the ; key, then release the key. This initiates a complete test of the calculators electronic circuitry. If everything is working correctly, within about 25 seconds (during which the word running flashes) the display should show 8,8,8,8,8,8,8,8,8,8, and all of the status indicators (except
Page: 194 of 209 Dimension: 14.8 cm x 21 cm
Appendix E: Battery, Warranty, and Service Information
the 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 calculators electronics are also performed if the = key or the z key is held down when ; is released. These tests are included in the calculator to be used in verifying that it is operating properly during manufacturing and service. If you had suspected that the calculator was not working properly but the proper display was obtained in step 2, it is likely that you made an error in operating the calculator. We suggest you reread the section in this handbook applicable to your calculation including, if appropriate, appendix A. If you still experience difficulty, write or telephone Hewlett-Packard at an address or phone number listed under Service (Page 197).

Page: 203 of 209 Dimension: 14.8 cm x 21 cm

204 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). Sets payment mode to End for compound interest calculations involving payments (page 37). 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). Stores or computes interest rate per compounding period (page 32). C Divides number in displayed X-register by 12 and stores the resulting value in the I-register (page 39). $ Stores or computes the present value (that is, the initial cash flow) of a financial problem (page 32). P Stores or computes payment amount (page 32).
M Stores or computes future value (final cash flow) of a financial problem (page 32). ! Amortizes x number of periods using values stored in PMT, i, PV, and the display. Updates values in PV and n (page 54). l Calculates the net present value of up to 20 uneven cash flows and initial investment using values stored with J, K, and a (page 58). L Calculates the internal rate of return (yield) for up to 20 uneven cash flows and initial investment using values stored with J, K, and a (page 63). J Initial cash flow. Stores contents of displayed X-register in R0, initializes n to zero, sets N0 to 1. Used at the beginning of a discounted cash flow problem (page 58). K Cash flow j. Stores the contents of X-register in Rj , increments n by 1, and sets Nj to 1. Used for all cash flows except the initial cash flow in a discounted cash flow problem (page 58).
V Calculates depreciation using straight-line method. (page 68). E Calculates bond price, given desired yield to maturity (page 67). S Calculates yield to maturity, given bond price (page 67). a Stores the number (from 1 to 99) of times each cash flow occurs as Nj. Assumes 1 unless otherwise specified (page 61). Calculates depreciation using sum-of-the-years-digits method (page 68). # Calculates depreciation using declining-balance method (page 68). Statistics CLEAR Clears statistical storage registers R1 through R6 and stack registers (page 76). _ Accumulates statistics using numbers from X- and Y-registers in storage registers R1 through R6 (page 76). ^ Cancels effect of numbers from X- and Y-registers in storage registers R1 through R6 (page 77).

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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). R Linear estimate (X-register), correlation coefficient (Y-register). Fits a line to a set of (x,y) data pairs entered using _, then extrapolates this line to estimate a y-value for a given x-value. Also computes strength of linear relationship (r) among that set of (x, y) data pairs (page 80). Q Linear estimate (X-register), correlation coefficient (Y-register). Fits a line to a set of (x, y) data pairs entered using _, then extra-polates this line to estimate an x-value for a given y-value. Also computes strength of linear relationship (r) among that set of (x,y) data pairs (page 80). y Computes reciprocal of number in displayed X-register (page 83). e Computes factorial [n(n1). 321] of number in displayed X-register (page 83). > Natural antilogarithm. Raises e (approximately 2.718281828) to power of number in displayed X-register (page 83). Computes natural logarithm (base e) of number in displayed X-register (page 83).
Number Alteration B Rounds mantissa of 10digit number in X-register to match the display (page 83). Leaves only the integer portion of number in displayed X-register by truncating fractional portion (page 83). T Leaves only the fractional portion of number in displayed X-register by truncating integer portion (page 84). Stack Rearrangement ~ Exchanges contents of X and Y-registers of stack (pages 74 and 172). d RolIs down contents of stack for viewing in displayed X-register (page 172). F Recalls number displayed before the previous operation back into the displayed X-register (pages 74 and 176).
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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 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. Active Keys: In Program mode only the following keys are active; they cannot be recorded in program memory. CLEAR Clear program. Clears program memory to all i00 instructions and resets calculator so operations begin at line 00 of program memory. Resets N to P08 r20 (page 95)

* Note

that the ; key is lower than the other keys to help prevent its being pressed

inadvertently.

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Section 1: Getting Started
Throughout this handbook, references to the functions shown on the keyboard in gold under the bracket labeled CLEAR appear throughout this handbook preceded by the word CLEAR (for example, The CLEARH function or Pressing fCLEARH ). If you press the f or g prefix key mistakenly, you can cancel it by pressing fCLEARX. This can also be pressed to cancel the ?, :, and i keys. (These keys are prefix keys in the sense that other keys must be pressed after them in order to execute the corresponding function.) Since the X key is also used to display the mantissa (all 10 digits) of a displayed number, the mantissa of the number in the display will appear for a moment after the X key is released. Pressing the f or g prefix key turns on the corresponding status indicator f or g in the display. Each indicator turns off when you press a function key (executing an alternate function of that key), another prefix key, or fCLEARX.

Keying in Numbers

To key a number into the calculator, press the digit keys in sequence, just as if you were writing the number on paper. A decimal point must be keyed in (using the decimal point key) if it is part of the number unless it appears to the right of the last digit.

Digit Separators

As a number is keyed in, each group of three digits to the left of the decimal point is automatically separated in the display. When the calculator is first turned on after coming from the factory or after Continuous Memory is reset the decimal point in displayed numbers is a dot, and the separator between each group of three digits is a comma. If you wish, you can set the calculator to display a comma for the decimal point and a dot for the three-digit separator. To do so, turn the calculator off, then press and hold down the. key while you press ;. Doing so again sets the calculator to use the original digit separators in the display.

Negative Numbers

To make a displayed number negative either one that has just been keyed in or one that has resulted from a calculation simply press (change sign). When the display shows a negative number that is, the number is preceded by a minus sign pressing removes the minus sign from the display, making the number positive.

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 two numbers should be keyed into the calculator in the order they would appear if the calculation were written down on paper left-to-right. After keying in the first number, press the \ key to tell the calculator that you have completed entering the number. Pressing \ separates the second number to be entered from the first number already entered. In summary, to perform an arithmetic operation: 1. Key in the first number. 2. Press \ to separate the second number from the first. 3. Key in the second number. 4. Press +,-,, or z to perform the desired operation. For example to calculate 13 2, proceed as follows: Keystrokes (RPN mode) 13 \ 2 z Display

13. 13.00 2. 6.50

Keys the first number into the calculator. Pressing \ separates the second number from the first. Keys the second number into the calculator. Pressing the operation key calculates the answer.
Notice that after you pressed \, two zeroes appeared following the decimal point. This is nothing magical: the calculators display is currently set to show two decimal places of every number that has been entered or calculated. Before you pressed \, the calculator had no way of knowing that you had completed entering the number, and so displayed only the digits you had keyed in. Pressing \ tells the calculator that you have completed entering the number: it terminates digit entry. You need not press \ after keying in the second number because the +,-, and z keys also terminate digit entry. (In fact, all keys terminate digit entry except for digit entry keys digit keys,., , and and prefix keys f, g, ?, :, and (.)
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Simple Arithmetic Calculations in ALG Mode
In ALG mode, any simple arithmetic calculation involves two numbers and an operation addition, subtraction, multiplication, or division. To do such a calculation on your hp 12c platinum, you tell the calculator the first number, then the operation to be performed, and then tell the calculator the second number. The answer is calculated when the equals key (}) is pressed. For example, to calculate 21.1 + 23.8, do the following: Keystrokes (ALG mode) OO 21.1+ 23.8 } Display

Storing and Recalling Numbers
To store the number from the display into a data storage register: 1. Press ? (store). 2. Key in the register number: 0 through 9 for registers R0 through R9, or.0 through.9 for registers R.0 through R.9. Similarly, to recall a number from a storage register into the display, press : (recall), then key in the register number. This copies the number from the storage register into the display; the number remains unaltered in the storage register. Furthermore, when this is done, the number previously in the display is automatically held inside the calculator for a subsequent calculation, just as the number in the display is held when you key in another number.
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Example: Before you leave to call on a customer interested in your personal computer, you store the cost of the computer ($1,250) and also the cost of a printer ($500) in data storage registers. Later, the customer decides to buy six computers and one printer. You recall the cost of the computer, multiply by the quantity ordered, and then recall and add the cost of the printer to get the total invoice. Keystrokes 1250?0 500?2 ; Later that same day Keystrokes (RPN mode) ; ::2 + Display Display

1,250.00 500.00

Stores the cost of the computer in R0. Stores the cost of the printer in R2. Turns the calculator off.
500.00 1,250.00 7,500.00 500.00 8,000.00
Turns the calculator back on. Recalls the cost of the computer to the display. Multiplies the quantity ordered to get the cost of the computers. Recalls the cost of the printer to the display. Total invoice.
Keystrokes (ALG mode) ; :+:2
500.00 1,250.00 6. 500.00 8,000.00
Turns the calculator back on. Recalls the cost of the computer to the display. Multiplies by the quantity ordered to get the cost of the computers. Recalls the cost of the printer to the display. Total invoice.
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Clearing Storage Registers
To clear a single storage register that is, to replace the number in it with zero merely store zero into it. You need not clear a storage register before storing data into it; the storing operation automatically clears the register before the data is stored. To clear all storage registers at once including the financial registers, the stack registers, and the LAST X register press fCLEARH.* This also clears the display. All storage registers are also cleared when Continuous Memory is reset (as described on page 86).

for dates when the Julian calendar was in use. The Julian calendar was standard in England and its colonies until September 14, 1752, when they switched to the Gregorian calendar. Other countries adopted the Gregorian calendar at various times.
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Example: If you purchased a 120-day option on a piece of land on 14 May 2004, what would be the expiration date? Assume that you normally express dates in the day-month-year format. Keystrokes g Display
Sets date format to day-month-year. (Display shown assumes date remains from preceding example. The full date is not now displayed because the display format is set to show only two decimal places, as described in Section 5.) Keys in the date and separates it from the number of days to be entered. The expiration date is 11 September 2004, a Saturday.

14.052004\

11,09,2004 6
When gD is executed as an instruction in a running program, the calculator pauses for about 1 second to display the result, then resumes program execution.
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Number of Days Between Dates
To calculate the number of days between two given dates: 1. Key in the earlier date and press \. 2. Key in the later date and press g. The answer shown in the display is the actual number of days between the two dates, including leap days (the extra days occurring in leap years), if any. In addition, the hp 12c platinum also calculates the number of days between the two dates on the basis of a 30-day month. This answer is held inside the calculator; to display it, press ~. Pressing ~ again will return the original answer to the display. Example: Simple interest calculations can be done using either the actual number of days or the number of days counted on the basis of a 30-day month. What would be the number of days counted each way, to be used in calculating the simple interest accruing from June 3, 2004 to October 14, 2005? Assume that you normally express dates in the month-day-year format. Keystrokes g Display
Sets date format to month-day-year. (Display shown assumes date remains from preceding example.) Keys in the earlier date and separates it from the later date. Keys in the later date. Display shows actual number of days. Number of days counted on the basis of a 30-day month.

In summary, to enter the amounts of the cash flows and the number of times they occur consecutively: 1. Press fCLEARH to clear the financial and storage registers. 2. Key in the amount of the initial investment, press if that cash flow is negative, then press gJ. 3. If the initial investment consists of more than one cash flow of the amount entered in step 2, key in the number of those cash flows, then press ga. If ga is not pressed, the calculator assumes that N0 is 1. 4. Key in the amount of the next cash flow, press if that cash flow is negative, then press gK. If the cash flow amount is zero in the next period, press 0gK. 5. If the amount entered in step 4 occurs more than once consecutively, key in the number of times that cash flow amount occurs consecutively, then press ga. If ga is not pressed, the calculator assumes that Nj is 1 for the CFj just entered. 6. Repeat steps 4 and 5 for each CFj and Nj until all cash flows have been entered. With the amounts of the cash flows and the number of times they occur consecutively stored in the calculator, NPV can be calculated by entering the interest rate and pressing fl, just as described earlier. Example: An investor has an opportunity to purchase a piece of property for $79,000; and he would like a 13.5% return. He expects to be able to sell it after 10 years for $100,000 and anticipates the yearly cash flows shown in the table below:

Cash Flow

$14,000 $11,000 $10,000 $10,000 $10,000
$9,100 $9,000 $9,000 $4,500 $100,000
Since two cash flow amounts ($10,000 and $9,000) are repeated consecutively, we can minimize the number of storage registers required by using the method just described.
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Keystrokes fCLEARH 79000gJ 14000gK 11000gK 10000gK 3ga 9100gK 9000gK 2ga 4500gK 100000gK :n 13.5 fl
0.00 79,000.00 14,000.00 11,000.00 10,000.00 3.00 9,100.00 9,000.00 2.00 4,500.00 100,000.00 7.00 13.50 907.77
Clears financial and storage registers. Initial investment (with minus sign for a negative cash flow). First cash flow amount. Next cash flow amount. Next cash flow amount. Number of times this cash flow amount occurs consecutively. Next cash flow amount. Next cash flow amount. Number of times this cash flow amount occurs consecutively. Next cash flow amount. Final cash flow amount. Seven different cash flow amounts have been entered. Stores i. NPV.
Since NPV is positive, the investment would increase the financial value of the investors assets by $907.77.
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Calculating Internal Rate of Return (IRR)

Page: 85 of 275 Dimension: 14.8 cm x 21 cm

Section 5

Additional Operating Features

Continuous Memory

The calculators 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. Furthermore, information in Continuous Memory is preserved for a short time when the batteries are removed, so that you can change the batteries without losing your data and programs. Continuous Memory may be reset if the calculator is dropped or otherwise traumatized, or if power is interrupted. You can also manually reset Continuous Memory as follows: 1. Turn the calculator off. 2. Hold down the - key, and press ;. When Continuous Memory is reset: All registers are cleared. Program memory consists of eight program lines, each containing the instruction g(000. Display format is set to the standard format with two decimal places. Date format is set to month-day-year. Payment mode is set to End. Arithmetic operation is set to RPN mode. Whenever Continuous Memory has been reset, the display will show Pr Error. Pressing any key will clear this message from the display.
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Section 5: Additional Operating Features

The Display

Status Indicators
Nine indicators that appear along the bottom of the display signify the status of the calculator for certain operations. These status indicators are described elsewhere in this handbook where the relevant operation is discussed.

Number Display Formats

When the calculator is first turned on after coming from the factory or after Continuous Memory has been reset, answers are displayed with two decimal places. Keystrokes (RPN mode) 19.8745632\ 5Keystrokes (ALG mode) 19.87456325} Display

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.
When only two decimal places are displayed, numbers are rounded to two decimal places: if the third digit is 5 through 9, the second digit is increased by one; if the third digit is 0 through 4, the second digit is not affected. Rounding occurs regardless of how many decimal places are displayed.

429000\ 987z

429,000.00 434.65
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Section 6

Statistics Functions

Accumulating Statistics

The hp 12c platinum can perform one- or two-variable statistical calculations. The data is entered into the calculator using the _ key, which automatically calculates and stores statistics of the data into storage registers R1, through R6. (These registers are therefore referred to as the statistics registers.) Before beginning to accumulate statistics for a new set of data, you should clear the statistics registers by pressing fCLEAR.* In one-variable statistical calculations, to enter each data point referred to as an x-value key the x-value into the display, then press _. In two-variable statistical calculations, to enter each data pair referred to as the x and y-values: 1. Key the y-value into the display. 2. Press \. 3. Key the x-value into the display. 4. Press _. Each time you press _, the calculator does the following: The number in R1 is increased by 1, and the result is copied into the display. The x-value is added to the number in R2. The square of the x-value is added to the number in R3. The y-value is added to the number in R4. The square of the y-value is added to the number in R5. The product of the x and y-values is added to the number in R6.
* This also clears the stack registers and the display. 93
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Section 6: Statistics Functions
The table below shows where the accumulated statistics are stored.

Register

R1 (and display) R2 R3 R4 R5 R6

Statistic

n: number of data pairs accumulated. x: summation of x-values. x : summation of squares of x-values.
y: summation of y-values. y summation of squares of y-values.
xy: summation of products of x-values and y-values.
Correcting Accumulated Statistics
If you discover you have entered data incorrectly, the accumulated statistics can easily be corrected. Simply key in the incorrect data point or data pair again as if it were new, but press g^ instead of _. Then enter the correct data point or data pair and press _.
Pressing g calculates the means (arithmetic averages) of the x-values ( x ) and of the y-values ( y ). The mean of the x-values appears in the display after g is pressed; to display the mean of the y-values, press ~. Example: A survey of seven salespersons in your company reveals that they work the following hours a week and sell the following dollar volumes each month. How many hours does the average salesperson work each week? How much does the average salesperson sell each month?

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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. The program line desired is specified by keying its three-digit line number into the program line containing the i instruction. When the i instruction is executed, program execution branches or goes to the program line specified and then continues sequentially as usual.
You have already seen a common use of branching: the gi000 instruction (that is stored in program memory after the program you key in) transfers execution to program line 000. A i instruction can be used to branch not only backward in program memory as in the case of gi000 and as illustrated above but also forward in program memory. Backward branching is typically done to create loops (as described next); forward branching is typically done in conjunction with a go or gm instruction for conditional branching (as described afterward).
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126 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. If you want to terminate the execution of a loop, you can include a go or gm 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. It will amortize one months payments each time or one years payments each time the loop is executed, depending on whether the number 1 or 12 is in the display when you start running the program. Before running the program, well initialize it by storing the required data in the financial registers just as we would do if we were amortizing a single payment manually. Well run the program for a $150,000 mortgage at 4.75% for 30 years, and well key 1 into the display just before running it in order to amortize monthly payments. For the first two passes through the loop well execute the program one line at a time, using , so that we can see the looping occurring; then well use t to execute the entire loop a third time before terminating execution. Keystrokes fs fCLEAR ?0 Display Sets calculator to Program mode.

017,43, 33,002 018,43, 33,000 019, 020, 021, 022, 023, 024, 025, 026, 12,000.31
Sets calculator to last line keyed into program memory. Ensures that second program is separated from first by i000.

Keys in program.

Halts program execution. Branches to beginning of program. Sets calculator back to Run mode. (Display shown assumes results remain from running program in previous example.)

027,43, 33,019

Keystrokes (ALG mode) fs gi.023 gi000
023,43, 33,002 024,43, 33,000
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Section 11: Multiple Programs
Keystrokes (ALG mode) b + 5 } t gi025 fs
025, 026, 027, 028, 029, 030, 031, 032, 12,000.00
Halts program execution. Branches to beginning of program. Sets calculator back to Run mode. (Display shown assumes results remain from running program in previous example.) Keys in program.

033,43, 33,025

Example 2: With the two programs now stored in program memory from the preceding examples (occupying 27 program lines in RPN mode and 33 lines in ALG mode), store the amortization program from Section 9(page 125). Since there are already two programs stored in program memory, well skip step 3 in the procedure above. Furthermore, since the amortization program ends with a loop, well skip steps 5 and 6. When the amortization program was stored at the beginning of program memory, the i instruction at the end of the program branched to the :0 instruction in line 002. In the RPN program, since the :0 instruction is now in line 029, well specify that line number with the i instruction in line 034. In the ALG program, since the :0 instruction is now in line 035, well specify that line number with the i instruction in line 041. Keystrokes (RPN mode) fs gi.027 Display Sets calculator to Program mode.
027,43, 33,019 Sets calculator to last line
keyed into program memory.
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152 Section 11: Multiple Programs
Keystrokes (RPN mode) ?0 :0 f! gu ~ gu gi029
028, 029, 030, 031, 032, 033,

Keys in program

034,43, 33,029
Keystrokes (ALG mode) fs gi.033 ?0 :0 f! gu ~ gu gi035
033,43, 33,025 Sets calculator to last line
034, 035, 036, 037, 038, 039,

040,43, 33,035

Page: 152 of 275 Dimension: 14.8 cm x 21 cm

Running Another Program

To run a program that does not begin with program line 001: 1. Press fs to set the calculator to Run mode. If the calculator is already in Run mode, skip this step. 2. Press gi followed by three digits that specify the first line of the program. 3. Press t. Example: Run the office-supplies program, now stored in the calculator beginning at program line 019 in RPN mode and line 025 in ALG mode, for the typewriter listing for $625. Keystrokes (RPN mode) fs gi019 625t Display

360.00 0.46 160,000.00 908.46
Months (into n) % monthly interest rate (into i). Loan amount (into PV). Monthly payment (calculated). Actual amount received by borrower (into PV). % monthly interest rate (calculated). Annual percentage rate.

156,800.00 0.47 5.68

Page: 157 of 275 Dimension: 14.8 cm x 21 cm
158 Section 12: Real Estate and Lending
Example 2: Using the same information as given in example 1, calculate the APR if the mortgage fee is $750 instead of a percentage. Keystrokes (RPN mode) f] g fCLEARG 30gA 5.5gC 160000$ P :$750$ 12 Keystrokes (ALG mode) f[ g fCLEARG 30gA 5.5gC 160000$ P :$-750 $ 12 Display
Months (into n) Percent monthly interest rate (into i). Loan amount (into PV). Monthly payment (calculated). Effective mortgage amount (into PV). Monthly interest rate (calculated). Annual percentage rate.

159,250.00 0.46 5.54

Example 3: Again using the information given in example 1, what is the APR if the mortgage fee is stated as 2 points plus $750? Keystrokes (RPN mode) f] g fCLEARG 30gA 5.5gC 160000$ P :$2b750-$ Keystrokes (ALG mode) f[ g fCLEARG 30gA 5.5gC 160000$ P :$-2b -750$ Display
Months (into n) Percent monthly interest rate (into i). Loan amount (into PV). Monthly payment (calculated). Effective mortgage amount (into PV).

156,050.00

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Keystrokes (RPN mode) 12

Keystrokes (ALG mode) 12

0.48 5.73

Monthly interest rate (calculated). Annual percentage rate.
Price of a Mortgage Traded at a Discount or Premium
Mortgages may be bought and/or sold at prices lower (discounted) or higher (at a premium) than the remaining balance of the loan at the time of purchase. Given the amount of the mortgage, the periodic payment, the timing and amount of the balloon or prepayment, and the desired yield rate, the price of the mortgage may be found. It should be noted that the balloon payment amount (if it exists) occurs coincident with, and does not include, the last periodic payment amount. Information is entered as follows: 1. Press g and fCLEARG. 2. Key in the total number of periods until the balloon payment or prepayment occurs; press n. (If there is no balloon payment, key in total number of payments and press n.) 3. Key in the desired periodic interest rate (yield) and press. 4. Key in the periodic payment amount; press P.* 5. Key in the balloon payment amount and press M.* (If there is no balloon payment, go to step 6.) 6. Press $ to obtain the purchase price of the mortgage. 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 $2,000. 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) f] g fCLEARG 72n Keystrokes (ALG mode) f[ Display

Book value. Life.

First year: depreciation.
Declining-Balance Depreciation
The following hp 12c platinum program calculates the declining-balance depreciation for the year desired with the acquisition date occurring at any time during the year.

fs fCLEAR z ?1 ~ ??0

000, 001, 002, 003, 004, 005, 006, 007, 008, 009, 30 0

fCLEAR z ?1 ~ ?2 1

000, 001, 002, 003, 004, 005, 006, 007, 008, 009, 1
Page: 176 of 275 Dimension: 14.8 cm x 21 cm
1 f# :1 ?3 :$ ~ $ :0 gm gi031 :2 gu :0 f# t 1 ?+0 ?+2 gi022 :2 gu :$
DISPLAY 010, 011, 012, 013, 014, 015, 016, 017, 018, 019, 020, 35
?f# :1 ?3 :$ ~ $ :0 gm gi034 :2 gu :0 f# t 1 ?+0 ?+2 gi025
DISPLAY 010, 011, 012, 013, 014, 015, 016, 017, 018, 019, 020, 021, 022, 023, 35
021,43, 33, 031 022, 023, 024, 025, 026, 027, 028,029,0 2
024,43, 33, 034 025, 026, 027, 028, 029, 030, 031,032,0 2
030,43,33, 022 031, 032, 033, 31 13

033,43,33, 025

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178 Section 13: Investment Analysis

:M :3 gi026 fs

DISPLAY 034, 035, 036, 3

:2 gu :$ :M :3 gi029 fs

DISPLAY 034, 035, 036, 037, 038, 039, 040, 36 3

037,43,33, 026

041,43,33, 029
n: Life FV: Salvage R3:1 Yr. Dep.
i: Factor R0: Used R4R.4: Unused
1. Key in the program. 2. Press fCLEARG. 3. Key in the book value then press $. 4. Key in the salvage value then press M. 5. Key in the declining-balance factor as a percentage then press. 6. Key in the life in years (an integer) then press n.
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RPN Mode: 7. Key in the year desired then press \. 8. Key in the number of months in first year* and press t. The display will show the amount of depreciation for the desired year. Press ~ to see the remaining depreciable value. If desired, press :$:3=~-:M- to find the total depreciation through the current year. ALG Mode: 7. Key in the year desired then press. 8. Key in the number of months in first year* and press t. The display will show the amount of depreciation for the desired year. Press ~ to see the remaining depreciable value. If desired, press :$=:3-~-:M to find the total depreciation through the current year. 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 gi000 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. What will the depreciation be during the first full accounting year (year 2) if the welder has a 6-year depreciable life, a salvage value of $8,000 and is depreciated using the declining-balance depreciation method? The declining-balance factor is 150%. Keystrokes (RPN mode) f] fCLEARG 50000$ 8000M 150 6n 2\ 4t Keystrokes (ALG mode) f[ fCLEARG 50000$ 8000M 150 6n 2 4t Display

When d (roll down) is pressed the number in each stack register is copied into the register below, and the number formerly in the X-register is copied into the T-register. Pressing d four times successively displays the numbers in the Y-, Z-, and T-registers and returns the numbers to their original registers.
* Note also that although the stack lifts when \ is pressed, it does not lift when a number is
entered after \ is pressed.
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One-Number Functions and the Stack
One-number mathematics and number-alteration functions y, r, , >, , e, B, , and T use only the number in the displayed X-register. When the key is pressed, the function is performed upon the number in the X-register, and the answer is then placed into the X-register. The stack does not lift, so the number formerly in the X-register does not get copied into the Y-register; but this number is copied into the LAST X register. The numbers in the Y-, Z-, and T-registers are not affected when a one number function is performed.
Two-Number Functions and the Stack
Two-number functions +, -, , z, q, b, , and Z use the numbers in both the X- and the Y-registers.

Mathematics Functions

To perform an arithmetic operation, the numbers are positioned in the X- and Y-registers just as you would write them vertically on paper: the number you would write on top goes in the Y-register, and the number you would write on the bottom goes in the X-register. For example, to do each of the four arithmetic calculations shown below, you would put the 8 in the Y-register (using \ and then key the 2 into the displayed X-register.)
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232 Appendix A: RPN and the Stack
When an arithmetic operation or q is performed, the answer is placed in the X-register, the number formerly in the X-register is copied into the LAST X register, and the stack drops. When the stack drops, the number in the Z-register is copied into the Y-register, and the number in the T-register is copied into the Z-register but also remains in the T-register. The diagram on the next page illustrates the stack operation when is calculated. (Assume that the stack and LAST X registers have already been loaded with the numbers shown as the result of previous calculations.)
When any of the three percentage functions is performed, the answer is placed in the X-register, the number formerly in the X-register is copied into the LAST X register, but the stack does not drop. The numbers in the Y-, Z-, and T-registers are not changed when a percentage function is performed.
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Appendix G

United Kingdom Calculations
The calculations for most financial problems in the United Kingdom are identical to the calculations for those problems in the United States which are described earlier in this handbook. Certain problems, however, require different calculation methods in the United Kingdom than in the United States, even though the terminology describing the problems may be similar. Therefore, it is recommended that you ascertain the usual practice in the United Kingdom for the financial problem you are solving. The remainder of this appendix describes three types of financial calculations for which the conventional practice differs significantly between the United Kingdom and the United States.

Mortgages

The amount of the repayments on home loans and mortgages offered by banks in the United Kingdom can usually be calculated as described under Calculating the Payment Amount, page 58. Building Societies in the United Kingdom, however, calculate the amount of these repayments differently. In general, the repayment amount of a Building Society mortgage is calculated as follows: first, the annual repayment amount is calculated using the annual interest rate; second, the periodic repayment amount is calculated by dividing the annual repayment amount by the number of repayment periods in one year. Furthermore, the calculations used by Building Societies are rounded; therefore, to match their scale repayment figures you would have to round your calculations accordingly.
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268 Appendix G: United Kingdom Calculations
Annual Percentage Rate (APR) Calculations
In the United Kingdom, the calculation of the Annual Percentage Rate of Charge (APR) in accordance with the United Kingdom Consumer Credit Act (1974) differs from the calculation of the APR in the United States. Unlike the practice in the United States, where the APR can be calculated by multiplying the periodic interest rate by the number of periods per year, in the United Kingdom the APR is calculated by converting the periodic interest rate to the effective annual rate, then rounding the result to one decimal place. With the periodic interest rate in the display and in the i register and the payment mode set to End, the effective annual rate can be calculated by pressing P, then keying in the number of compounding periods per year and pressing w0$M. Pressing f1 will then display the rounded APR.