(17B/19B) GPM: initial payment

[Albert Chan]

(05-27-2024 08:38 PM)Albert Chan Wrote:  pv/pmt = -1/c12 - q/c12 - q^2/c12 - q^3/c12 - q^4/c12 - q^5/c300

Hi, Werner

Good tip about using (q-1) as rate.

Last term is FV of (N=5, I=q-1, PV=1/c300, PMT=0)
Others sum to FV of (N=5, I=q-1, PV=0, PMT=1/c12)

All terms have same sign, there is no cancellation issue.
We can combine them all in 1 TVM calculation.

q = s / (1+APY)
q-1 = ((s-1)-APY) / (1+APY)

lua> i, pv = 0.01, 6e4
lua> K = fn'i,n: expm1(log1p(i)*n)' -- = (1+i)^n - 1
lua> USPV = fn'i,n: -K(i,-n)/i'          -- = 1 / cn
lua> APY = K(i,12)
lua> tvm(5, (.075-APY)/(1+APY), USPV(i,300), USPV(i,12), nil) -- = pv/pmt
-126.3623094884877
lua> pv / _ -- = pmt
-474.82512976281373