Finance problems (TVM) on hp 49G+ hp 50G Periods and compounds per year are different

[Albert Chan]

(05-13-2024 01:35 AM)Karinne Wrote:  In finance mode, when I want to solve TVM problems, my calculator does not have the option for payments per year (P/Yr) and compounding per year (C/Yr), separately.

Found the relation of (I/Yr, P/Yr, C/Yr) for per period effective interest rate.

i = (1 + (I/Yr)/(C/Yr)) ^ ((C/Yr)/(P/Yr)) - 1

If (P/Yr) = (C/Yr), it reduced to simple ratio: i = (I/Yr) / (P/Yr)

We can use log1p/expm1 for better accuracy.

i = expm1(log1p((I/Yr)/(C/Yr)) * (C/Yr)/(P/Yr))
(I/Yr) = expm1(log1p(i) * (P/Yr)/(C/Yr)) * (C/Yr)

Example:

lua> ipy, ppy, cpy = .05, 12, 3 -- (I/Yr), (P/Yr), (I/Yr)
lua> i = expm1(log1p(ipy/cpy) * cpy/ppy)
lua> i
0.004140875317607807
lua> expm1(log1p(i) * ppy/cpy) * cpy -- == ipy
0.05

lua> n, pv, fv = 60, 30000, 0
lua> tvm(n, i, pv, nil, fv) -- solve for pmt
-565.7117263797815

HP Prime TVM app:
N=60, PV=30000, FV=0, I%Yr=5.00, P/Yr=12, C/Yr = 3, END=1      → PMT = -565.71