(71B) calculate interest rate

[Albert Chan]

Some improvements over my 3-points fit rate finder (post #6)

• FNF may be more accurate, using Fused Multiply Add.
  FNF = FMA(EXPM1(N*LOGP1(I))/I, P*I+M, F+P)
• FNF(0) singularity removed, now FNF(0) = F+P + M*N
• We use harmonic mean of I1,I2 for X1.
• We use (0, FNF(0)) and (X1,Y1) to estimated X2.
  But, point "0" might be too far, giving bad interpolated rate.
  Instead of interpolation for Y=0 for X2, we cut the corrections in half (thus the factor 0.5)

Quote:10 INPUT "n, fv, pv, pmt ? ";N,F,P,M
20 DEF FNS(X1,Y1,X2,Y2)=X1-Y1*(X2-X1)/(Y2-Y1)
30 DEF FNF(I)
40 A=N @ IF I THEN A=EXPM1(N*LOGP1(I))/I
50 B=P*I+M @ A0=A*B
60 A1=A*1000001 @ A1=A+A1-A1 @ A=A-A1
70 B1=B*1000001 @ B1=B+B1-B1 @ B=B-B1
80 FNF=(F+P+A0)-(A0-A1*B1-A1*B-B1*A-A*B)
90 END DEF
100 X1=4*(F+P+M*N)/((N-1)*(F-M*N)-(3*N+1)*P)
110 Y1=FNF(X1) @ DISP X1,Y1 @ IF Y1=0 THEN END
120 X2=X1+.5*X1*Y1/(F+P+M*N-Y1)
130 Y2=FNF(X2) @ DISP X2,Y2 @ IF Y2=0 THEN END
140 X3=FNS(X1,Y1,X2,Y2)
150 Y3=FNF(X3) @ DISP X3,Y3 @ IF Y3=0 THEN END
160 E3=-Y3*FNS((X3-X2)/(Y3-Y2),Y2,(X3-X1)/(Y3-Y1),Y1)
170 X1=X2 @ Y1=Y2 @ X2=X3 @ Y2=Y3 @ X3=X3+E3
180 IF .00001*E3+X3-X3 THEN 150
190 DISP X3

>RUN
n, fv, pv, pmt ? 168, 10925.76, 0, -45
4.36103281596E-3     -190.348820115
4.24431571126E-3     -70.197349875
4.17612485668E-3     -.75216795
4.17538334438E-3     -.000041145
4.17538330381E-3
>RUN
n, fv, pv, pmt ? 600, 1e6, 0, -250
4.93576250272E-3     78873.4148425
5.18818567872E-3     -26668.4502875
5.12440307537E-3     1206.531985
5.12720670893E-3     -1.0521275
5.12720426781E-3     .0000175
5.12720426785E-3
>RUN
n, fv, pv, pmt ? 30,50000,1000,-1000
3.76850605653E-2     -930.964898075
3.68851990742E-2     -289.785021642
3.65236969622E-2     -3.12429013971
3.65197437154E-2     -1.49842044802E-4
3.65197435258E-2