PC-1211, PC-1250, etc. TVM

[Albert Chan]

(07-11-2022 09:08 PM)Albert Chan Wrote:  I just realized there is no financial function called NPMT (we do have NPV, NFV)
We can define NPMT as a TVM function that work the same way, if time direction reversed.

NPMT = C*pv + C(n=-n)*fv + n*pmt

NPMT tends to be more "straight" than (NPV, NFV), with values inside (NPV, NFV)
Thus, f = NPMT/n = 0 is great for solving rate x, using Newton's method.

Just want to clear up meaning of NPMT. It is not "Net Payment" ... more like "N Payments".
Function used for rate search is f = NPMT/n (sometimes refer as npmt function)

Technically, time-symmetry is exactly what you expected when viewing film backwards:

{n,i,pv,pmt,fv} ↔ {-n,i,fv,-pmt,pv}

NPMT is time-symmetrical (same value with time-symmetry transform)
npmt is not. Because of n denominator, we had to negate it to preserve the same result.

{n,i,pv,pmt,fv} ↔ {-n,i,fv,-pmt,pv} --> negate --> {-n,i,-fv,pmt,-pv}

Warning: To count sign changes for possible solutions, we should use (n*pmt)
Time symmetry will give same sign changes either way, even if negated.

{pv,n*pmt,fv} ↔ {fv,(-n)*(-pmt),pv} = {fv,n*pmt,pv}