(17B/19B) GPM: initial payment

[Werner]

Taking the original equation, we can make it simpler:

Code:

GPM:PV+PMTxΣ(T:0:N:1:USPV(I%/12:12xIF(T<N:1:M-N))xSPFV(G%:T)/SPFV(I%/12:Tx12))

rationale, shown for N=5:
PMTx
T
0 USPV(I%/12,12)*SPFV(G%,0)/SPFV(I%/12,0)
1 USPV(I%/12,12)*SPFV(G%,1)/SPFV(I%/12,12)
2 USPV(I%/12,12)*SPFV(G%,2)/SPFV(I%/12,24)
3 USPV(I%/12,12)*SPFV(G%,3)/SPFV(I%/12,36)
4 USPV(I%/12,12)*SPFV(G%,4)/SPFV(I%/12,48)
5 USPV(I%/12,(M-N)x12)*SPFV(G%,5)/SPFV(I%/12,60)

USPV compounds the payments made, either 12 or 12*(M-N)
xSPFV G% multiplies by G% every year
/SPFV I%/12 brings it to the present

drawback is that it recalculates USPV(I%/12,12) N-1 times, so execution will be slower.

Cheers, Werner