PC-1211, PC-1250, etc. TVM

[Albert Chan]

Hi, robve

Conditions required to make sign change suffices, without more iterations.

1. use NPMT formula (equivalent splitted loan method also OK)
2. use true derivative, not secant line slope.
3. use edge rate, in END mode, either [M/-P, M/F]

I modified my 2nd post (#9), with Plus42 "smaller" edge as guess.
I also make calculations more accurate, just to show it is hard to have f overshoot.

10 INPUT "B,N,P,M,F? ";B,N,P,M,F @ B=B*M
20 DEF FNF(I) @ S=-EXPM1(LOGP1(I)*-N)
25 D=(P+F)/S*(1-N*(1-S)/(S+S/I))+(B-F)
30 FNF=(P+F)*I/S+(B-F)*I+M @ END DEF ! FNF=NPMT
40 X=(ABS(P)<ABS(F))*(P+F)-B @ I=M/(X-P) @ Y=FNF(I)
50 H=-Y/D @ I=I+H @ Y=FNF(I) ! Newton's method
60 DISP 100*I,Y @ IF I+H*H<>I THEN 50

Code:

>run
B,N,P,M,F? 1,40,900,-40,-1000
 4.7524512828        -.0080716937
 4.75336718645       -.0000000187
 4.75336718857        0
>run
B,N,P,M,F? 1,40,900,-400,-1000
 79.9999999644       -.000000183
 80.000000001         0  
>run
B,N,P,M,F? 1,40,900,1000,-1000
-50                   0
>run
B,N,P,M,F? 0,360,0,-1000,1e6
 .313028391458        504.47068745
 .47127071031         62.96905733
 .497374290777        1.51994785
 .498036166886        .00095669
 .498036584011        0