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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><y
17- 34
Press RCL, then 1
18- 45 1
Press RCL, then n
19- 45 11
Press CHS
20- 16
Press yx
21- 21
Press STO, then 3
22- 44 3
Press [-]
23- 30
Press RCL, then 2
24- 45 2
Press ÷
25- 10
Press STO, then 4
26- 44 4
Press RCL, then 5
27- 45 5
Press x
28- 20
Press STO, then 6
29- 44 6
Press x><y
30- 34
Press 2
31- 2
Press x><y
32- 34
Press g, then x<=y
33- 43 34
Press g, GTO, then 61
34- 43,33 61
Press 3
35- 3
Press x><y
36- 34
Press g, then x<=y
37- 43 34
Press g, GTO, then 47
38- 43,33 47
Press RCL, then 6
39- 45 6
Press RCL, then PV
40- 45 13
Press +
41- 40
Press RCL, then 3
42- 45 3
Press ÷
43- 10
Press CHS
44- 16
Press STO, then FV
45- 44 15
Press g, GTO, then 00
46- 43,33 00
Press RCL, then FV
47- 45 15
Press RCL, then 3
48- 45 3
Press x
49- 20
Press RCL, then PV
50- 45 13
Press +
51- 40
Press RCL, then 4
52- 45 4
Press ÷
53- 10
Press RCL, then 1
54- 45 1
Press RCL, then 0
55- 45 0
Press yx
56- 21
Press ÷
57- 10
Press CHS
58- 16
Press STO, then PMT
59- 44 14
Press g, GTO, then 00
60- 43,33 00
Press RCL, then FV
61- 45 15
Press RCL, then 3
62- 45 3
Press x
63- 20
Press RCL, then 6
64- 45 6
Press +
65- 40
Press CHS
66- 16
Press STO, then PV
67- 44 13
Press g, GTO, then 00
68- 43,33 00
Press RCL, then 5
69- 45 5
Press RCL, then FV
70- 45 15
Press RCL, then 2
71- 45 2
Press x
72- 20
Press [-]
73- 30
Press RCL, then 5
74- 45 5
Press RCL, then PV
75- 45 13
Press RCL, then 2
76- 45 2
Press x
77- 20
Press +
78- 40
Press ÷
79- 10
Press g, then LN
80- 43 23
Press RCL, then 1
81- 45 1
Press g, then LN
82- 43 23
Press ÷
83- 10
Press STO, n, f, then P/R
84- 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
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><y
56- 34
Press EEX
57- 26
Press CHS
58- 16
Press 8
59- 8
Press g, then x<=y
60- 43 34
Press g, GTO, then 05
61- 43,33 05
Press RCL, then 3
62- 45 3
Press EEX
63- 26
Press 2
64- 2
Press x
65- 20
Press ENTER
66- 36
Press STO, i, f, then P/R
67- 44 12
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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