(17B/19B) GPM: initial payment

[Albert Chan]

(05-30-2024 03:14 AM)Gil Wrote:  I thought wrongly that, in graduated approach,
during first year payments Pi (P1, P2... P12) = fix amount =P
during the 2nd year P13, P14... P24=fix amount = P. 1.075
etc
But, as I deduce from your explanations, it's not the case.

You are right, that was how GPM is normally setup.
I was just showing what happen if compounding and payment growth are in sync (monthly)

We could also solve GPM payment by assuming payment is in yearly basis.
This setup, compounding and payment growth are now in sync (yearly)

lua> K = fn'i,n: expm1(log1p(i)*n)' -- = (1+i)^n - 1
lua> USFV = fn'i,n: K(i,n)/i' -- = 1 / dn
lua> USPV = fn'i,n: -USFV(i,-n)' -- = 1 / cn

lua> s, i, pv = 1.075, 0.01, 6e4
lua> I = K(i,12) -- = APY
lua> tvm(5, (s-1-I)/(1+I), USPV(I,25), USPV(I,1), nil) -- = pv/pmt
-9.96351503776498
lua> pmt = pv / _

lua> pmt -- yearly payment
-6021.971138958528
lua> pmt / USFV(i,12) -- equivalent monthly payment
-474.82512976281373