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# HP 12c Calculator - Actuarial Calculations

Introduction
This collection of programs calculates the compound interest function n, i, PV, PMT, and FV using the actuarial method. This means that the value for n can be any real number. Calculations using a negative or non-integer value for n produce a mathematically correct result, but this has no simple useful interpretation.
The first program calculates n, PV, PMT, or FV. The second program, a shorter version of the first program, calculates only n. The third program calculates i.
Program to calculate n, PV, PMT, and FV
 Key (RPN mode) Display Press f, P/R, f, then PRGM 00- Press STO, then 4 01- 44 4 Press 1 02- 1 Press RCL, then i 03- 45 12 Press % 04- 25 Press STO, then 2 05- 44 2 Press + 06- 40 Press STO, then 1 07- 44 1 Press RCL, then 0 08- 45 0 Press yx 09- 21 Press RCL, then PMT 10- 45 14 Press x 11- 20 Press STO, then 5 12- 44 5 Press 1 13- 1 Press RCL, then 4 14- 45 4 Press g, then x<=y 15- 43 34 Press g, GTO, then 69 16- 43,33 69 Press x>
Registers
 Register Use n Used i Used PV Used PMT Used FV Used R0 0 or 1 R1 1 + i R2 i R3 Used R4 Used R5 Used R6 Used R7 Unused
Instructions for n, PV, PMT, FV program
1. Key in the n, PV, PMT, FV Program listed above.
2. Press f, then CLX to clear out the data and finance registers.
3. Store 0 in register 0 for END mode; store 1 in register 0 for BEGIN mode.
4. Key in the periodic interest rate and press i
5. Key in any three of the following variables. Use the cash flow convention (money received is positive; money paid out is negative).
1. Key in the total number of periods and press n
2. Key in present value and press PV
3. Key in the periodic payment and press PMT
4. Key in the future value and press FV
6. To calculate n, press 1, then R/S
7. To calculate PV, press 2, then R/S
8. To calculate PMT, press 3, then R/S
9. To calculate FV, press 4, then R/S
10. For subsequent problems, return to step 2 and change the values as needed.
Example of calculating monthly payments necessary to amortize a loan
A \$1000 loan has monthly payments of \$80. If the annual interest rate is 9 percent, how many payments are necessary to amortize the loan? The payments are made at the END of each period.
 Key (RPN mode) Display Description Press f, then CLX 0.00 Clears the data and finance registers Press 0, STO, then 0 0.00 Sets END mode Press 1000, CHS, then PV -1,000.00 Stores the loan amount Press 9, g, then 12÷ 0.75 Stores the periodic interest rate Press 80, then PMT 80.00 Stores the payment amount Press 0, then FV 0.00 Stores the ending amount Press 1, then R/S 13.17 Calculates the number of monthly payments
Program to calculate i
 Key (RPN mode) Display Press f, P/R, f, then PRGM 00- Press [.] 01- 48 Press 0 02- 0 Press 1 03- 1 Press STO, then 3 04- 44 3 Press 1 05- 1 Press RCL, then 3 06- 45 3 Press 1 07- 1 Press + 08- 40 Press STO, then 1 09- 44 1 Press RCL, then n 10- 45 11 Press CHS 11- 16 Press yx 12- 21 Press STO, then 2 13- 44 2 Press [-] 14- 30 Press RCL, then 3 15- 45 3 Press [/] 16- 10 Press RCL, then 3 17- 45 3 Press RCL, then 0 18- 45 0 Press x 19- 20 Press 1 20- 1 Press + 21- 40 Press x 22- 20 Press RCL, then PMT 23- 45 14 Press x 24- 20 Press RCL, then PV 25- 45 13 Press + 26- 40 Press RCL, then FV 27- 45 15 Press RCL, then 2 28- 45 2 Press x 29-23 20 0 Press + 30-23 40 1 Press RCL, then 2 31-23 45 2 Press RCL, then 1 32- 45 1 Press [/] 33- 10 Press RCL, then n 34- 45 11 Press x 35- 20 Press STO, then 4 36- 44 4 Press 1 37- 1 Press RCL, then 2 38- 45 2 Press [-] 39- 30 Press RCL, then 3 40- 45 3 Press [ ] 41- 10 Press [-] 42- 30 Press RCL, then PMT 43- 45 14 Press RCL 44- 45 3 Press [/] 45-24 10 6 Press x 46- 20 Press RCL, then FV 47- 45 15 Press RCL, then 4 48- 45 4 Press x 49- 20 Press [-] 50- 30 Press [/] 51- 10 Press STO, [-], then 3 52- 44,30 3 Press ENTER 53- 36 Press CHS 54- 16 Press g, then x<=y 55- 43 34 Press x>
Registers
 Register Use n Used i Used PV Used PMT Used FV Used R0 0 or 1 R1 1 + i R2 (1 + i) -n R3 i guess R4 Used R5-R0 Unused
Instructions for i program
1. Key in the i Program listed above.
2. Press f, then CLX
3. Store 0 in register 0 for END mode; store 1 in register 0 for BEGIN mode.
4. Key in three or four of the following variables. Use the cash flow sign convention (money received is positive; money paid out is negative).
1. Key in the total number of periods and press n
2. Key in the present value and press PV
3. Key in the periodic payment and press PMT
4. Key in the future value and press FV
5. Press R/S to run the program to calculate the periodic interest rate.
6. For subsequent problems, return to step 2 and change the values as needed.
Example of calculating interest rate required for growth
A savings account has a balance of \$1000. What annual interest rate is required to double the money in 51/2 years?
##### note:
Key in the i program before running this example.
 Key (RPN mode) Display Description Press f, then CLX 0.00 Clears out the data and finance registers Press 0, STO, then 0 0.00 Sets END mode Press 1000, CHS, then PV -1,000.00 Stores the present value Press 2000, then FV 2,000.00 Stores the ending value Press 5.5, then n 5.50 Stores the number of periods Press 0, then PMT 0.00 Stores 0 into PMT Press R/S 13.43 Calculates annual interest rate
Program to calculate n
 Key (RPN mode) Display Press f, P/R, f, then PRGM 00- Press 1 01- 1 Press RCL, then i 02- 45 12 Press % 03- 25 Press STO, then 2 04- 44 2 Press + 05- 40 Press STO, then 1 06- 44 1 Press RCL, then 0 07- 45 0 Press yx 08- 21 Press RCL, then PMT 09- 45 14 Press x 10- 20 Press STO, then 3 11- 44 3 Press RCL, then FV 12- 45 15 Press RCL, then 2 13- 45 2 Press x 14- 20 Press [-] 15- 30 Press RCL, then PV 16- 45 13 Press RCL, then 2 17- 45 2 Press x 18- 20 Press RCL, then 3 19- 45 3 Press + 20- 40 Press ÷ 21- 10 Press g, then LN 22- 43 23 Press RCL, then 1 23- 45 1 Press g, then LN 24- 43 23 Press ÷ 25- 10 Press STO, n, f, then P/R 26- 44 11
Registers
 Register Use n Used i Used PV Used PMT Used FV Used R0 0 or 1 R1 1 + i R2 i R3 Used R4 - 5 Used
Instructions for n program
1. Key in the n program listed above.
2. Press f, then CLX
3. Store 0 in register 0 for END mode; store 1 in register 0 for BEGIN mode.
4. Key in the periodic interest rate and press i
5. Key in the following variables. Use the cash flow sign convention (money received is positive; money paid out is negative).
1. Key in the present value and press PV
2. Key in the periodic payment and press PMT
3. Key in the future value and press FV
6. Press R/S to calculate n, the total number of periods.
7. For subsequent problems, return to step 2 and change the values as needed.
Example of calculating compound interest
A deposit of \$150 is made each month in an account paying 6.5 percent, compounding monthly. How long will it take to accumulate \$20,000? Assume END mode.
##### note:
Key in the n program before running this example.
 Key (RPN mode) Display Description Press f, then CLX 0.00 Clears out the data and finance registers Press 0, STO, then 0 0.00 Sets END mode Press 6.5, g, then i 6.50 Stores the annual interest rate Press 0, then PV 0.00 Stores the beginning value Press 150, CHS, then PMT -150.00 Stores the monthly deposits Press 20000, then FV 20,000.00 Stores ending value Press R/S 100.63 Calculates the number of periods

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