(42S) TVM Program for HP 42S

[Jeff_Kearns]

(05-23-2014 11:02 AM)Ender Wrote:  A TVM program for HP 42S.

There is a much shorter (albeit less extravagant) 31 step version here for those who don't wish to enter 253 lines of code:

An accurate TVM equation written as a program for the HP42S Solver.
n number of periods
i interest rate
PMT periodic payment
PV present value
FV future value
B/E BEGIN/END
Solve equation:
PMT*(i1-1)*(1/i+p)+PV*i1+FV=0

where (i1-1) = e1^(n*ln1(i))
and i1 = e^(n*ln1(i))
and ln1(x) = ln(1+x)
and e1(x) = e^x-1
p=0 for END, p=1 for BEGIN

The use of ln1+x and e^x-1 prevents the loss of significant digits for small values of i. Consider these extreme examples for accuracy checking:
Example 1:
n=63
i=0.00000161
PV=0
PMT=-1,000,000
END Mode (set B/E=0 in Solver)
Solving for FV:
HP 42S: 63,000,031.4434 (correct is 63,000,031.4433)
Example 2:

n=31536000
i=10/n
PV=0
PMT=-0.01
END Mode
Solving for FV:
HP 42S: 331,667.006689 (correct is 331,667.006691)

You might compare these results using the "normal" TVM equation, found in many manuals
E.g. using the TVM equation in the 42S manual, we get
62,921,744.4422 and 311,565.594018 respectively.

The program:
00 {91-Byte Prgm }
01 LBL "TVM"
02 MVAR "N"
03 MVAR "I%"
04 MVAR "PV"
05 MVAR "PMT"
06 MVAR "FV"
07 MVAR "B/E"
08 RCL "I%"
09 100
10 /
11 LN1+X
12 RCL* "N"
13 E^X-1
14 RCL* "PMT"
15 RCL "I%"
16 100
17 /
18 1/X
19 RCL+ "B/E"
20 *
21 RCL "PV"
22 RCL "I%"
23 100
24 /
25 LN1+X
26 RCL* "N"
27 E^X
28 *
29 +
30 RCL+ "FV"
31 END