Looking for TVM contributions

[robve]

(06-17-2024 06:37 PM)SlideRule Wrote:  from an unknown but astute source;

EXCEL uses a slightly different TVM equation in solving for interest rate … making it most useful

PV(1+RATE)^NPER + PMT (1+RATE*TYPE)[{(1+RATE)^NPER} - 1] / RATE + FV = 0

This equation holds true i.e. it equals ZERO when at least one or at most two of the three variables of PV, FV, and PMT are negative.

BEST!
SlideRule

Assuming TYPE is 0 for END and 1 for BGN, then we recognize PV and FV are switched and their signs inverted and N is inverted:
PV*S + PMT*K*R/I + FV = 0
with K=1+B*I and R=EXPM1(-N*LNP1(I)) and S=R+1

Compare this to

FV = (K*PMT*R/I-PV)/S
K*PMT*R/I - PV - FV*S = 0

This gives the same TVM problem.

EDIT: I just checked with the Hybrid solver:

./tvm 328 '?' 35000 -324 0
n=328.000000 pv=35000.000000 pmt=-324.000000 fv=0.000000
evals=6, I%=0.872056914834067998%, FVerror=1.3e-10

./tvm -328 '?' 0 -324 -35000
n=-328.000000 pv=0.000000 pmt=-324.000000 fv=-35000.000000
evals=5,I%= 0.872056914834067887%, FVerror=0

So this aligns with the observation Albert made.

- Rob