(17B/19B) GPM: initial payment

[Werner]

Made the 12C procedure a lot simpler, using an alternate version of the equation (without BEG or FV):

0 = PV/USFV(K%,NG) + PMT*(USPV(I%,NP) + USPV(I%,N-NP*NG)/USPV(K%,NG))

P := USPV(I%,NP);
K% := G%*SPPV(I%:NP)-I%*P;
PMT := -PV/(USFV(K%,NG)*(P + USPV(I%:N-NP×NG)/USPV(G(K%):NG));

17B equation:

Code:

GPM:PV/USFV(L(K%:G%×SPPV(I%:NP)-I%×L(P:USPV(I%:NP))):NG)+PMT×(G(P)+USPV(I%:N-NP×NG)/USPV(G(K%):NG))

12C procedure (reuses values on the stack, so make sure to follow it to the letter):

 variable value key            result        description
               [f] [CLEAR FIN]
               [g] [END]
 NP        12  [N]
 I%        1   [i]
               [STO] [PMT]
 G%       7.5  [CHS] [FV]
               [PV]           -4.599208284   K%
               [STO] [i]
 NG        5   [N]
           0   [PV]
           1   [PMT]
               [FV]           -4.560749934  -USFV(K%:NG)
           0   [FV]
               [PV]           -5.771336094  -USPV(K%:NG)
 N-NP*NG  300  [N]
 I%        1   [i]
               [PV]          -94.94655125   -USPV(I%:N-NP*NG)
               [X<>] [/]      16.45139872
 NP        12  [N]
               [PV]          -11.25507747   -USPV(I%:NP)
               [-] [x]      -126.3623095
 PV     60000  [X<>Y] [/]   -474.8251297    PMT

Cheers, Werner