This program is Copyright © 1978 by Hewlett-Packard and is used here by permission. This program was originally published in "HP-38E/38C Personal Finance Applications" book. This program was transcribed by Kris Collins.
This program is supplied without representation or warranty of any kind. Hewlett-Packard Company and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.
Finding the true rate of return on an investment portfolio where variable amounts are invested or withdrawn at indefinite or irregular intervals is a complicated calculation. However, it is a highly useful tool in money management.
This program uses "Fisher's algorithm", a powerful technique to solve for the true realized rate of return.
Notes:
Reference:
1) Lawrence Fisher, "An Algorithm for finding Exact
Rates of Return", The JOURNAL OF BUSINESS, University of Chicago Press,
Volume XXXIX No. 1 part 2, January 1966.
g P/R g CLP | 00- | g LASTX | 25 31 |
RCL PMT | 01-24 14 | g FRAC | 30-25 61 |
f Change DAYS | 02-24 41 | 2 | 31-2 |
3 | 03-3 | g y^{x} | 32-25 21 |
6 | 04-6 | f SQRT X | 33-25 21 |
5 | 05-5 | g EEX | 34-25 32 |
0 | 06-0 | 2 | 35-2 |
0 | 07-0 | x | 36-61 |
/ | 08-71 | ENTER | 37-31 |
RCL PV | 09-22 13 | ENTER | 38-31 |
g x<>y | 10-25 5 | RCL i | 39-22 12 |
g GTO 15 | 11-25 7 15 | x | 40-61 |
/ | 12-51 | g e^{x} | 41-25 22 |
g CF_{i} | 13-25 14 | RCL PV | 42-22 13 |
g GTO 00 | 14-25 7 00 | x | 43-61 |
x<>y | 15-33 | STO / 0 | 44-21 51 0 |
- | 16-41 | x | 45-61 |
g GTO 13 | 17-25 7 13 | STO / 1 | 46-21 51 1 |
1 | 18-1 | RCL n | 47-22 11 |
0 | 19-0 | 3 | 48-3 |
n | 20-11 | g x<>y | 49-25 5 |
0 | 21-0 | g GTO 24 | 50-25 7 24 |
STO 0 | 22-21 0 | RCL i | 51-22 12 |
STO 1 | 23-21 1 | RCL FV | 52-22 15 |
RCL g CF_{i} | 24-22 25 14 | RCL 0 | 53-22 0 |
g x=0 | 25-25 6 | - | 54-41 |
g GTO 24 | 26-25 7 24 | RCL 1 | 55-22 1 |
f INTGR | 27-24 61 | / | 56-71 |
PV | 28-13 | / | 57-51 |
i | 58-12 | CHS | 66-32 |
g LASTX | 59-25 31 | g x<>y | 67-25 5 |
g PSE | 60-25 4 | g GTO 18 | 68-25 7 18 |
2 | 61-2 | 1 | 69-1 |
g y^{x} | 62-25 21 | RCL i | 70-22 12 |
f SQRT x | 63-24 21 | f %T | 71-24 22 |
g EEX | 64-25 32 | g P/R | |
7 | 65-7 |
R_{0} Sum numerator | R_{1} Sum denominator | R_{2} CF_{1} | R_{3} CF_{2} |
R_{4} CF_{3} | R_{5} CF_{4} | R_{6} CF_{5} | R_{7} CF6 |
R_{8} CF_{7} | R_{9} CF_{8} | R_{.0} CF_{9} | R_{n} n |
R_{i} i_{k} | R_{PV} T | R_{PMT} p_{j} | R_{FV} V_{T} |
Instructions:
Example:
You invest in a pension fund and after anumber of year you are told that the fund value was 9,050 dollars on 7/01/1977. Determine the effective (continuously compounded) and nominal rate of return from the record of your transactions which are as follows:
an investment of $4,150 on 1/01/1972;
an investment of $2,005 on 1/01/1973;
a withdrawal of $950 on 1/01/1974;
a withdrawal of $3,111 on 1/01/1975;
an investment of $2,000 on 10/01/1975;
an investment of $2,005 on 1/01/1976; and
a final investment of $1,000 on 7/01/1976.
D.MY/M.DY = M.DY | |
f CLEAR ALL | 0.00 |
7.011977 PMT | 7.01 |
9050 FV | 9,050.00 |
.1 I | 0.10 |
2 N | 2.00 |
4150 PV | 4,150.00 |
1.011972 R/S | 4,150.06 |
2005 PV | 2,005.00 |
1.011973 R/S | 2,005.04 |
950 CHS PV | -950.00 |
1.011974 R/S | -950.03 |
3111 CHS PV | -3,111.00 |
1.011975 R/S | -3,111.02 |
2000 PV | 2,000.00 |
10.011975 R/S | 2,000.02 |
2005 PV | 2,005.00 |
1.011976 R/S | 2,005.01 |
1000 PV | 1,000.00 |
7.011976 R/S | 1,000.01 |
g GTO 18 | |
R/S | (-.04) Differences between |
(-0.004) successive approximations | |
(-0.00005) of the correct interest rate. | |
(-0.00000001) | |
5.90 effective continuous rate |
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