TVM solve for interest rate, revisited

[Albert Chan]

(05-13-2022 09:31 PM)Albert Chan Wrote:  Let t = tanh(n/2*log1p(x)), put Ce back to NPMT:

f = A*x/t + B*x + pmt

f = 0 → x = -pmt / (A/t + B)

t = -1 .. 1      → x = pmt/fv .. -pmt/pv

I made an error here.
If t = -A/B is within ± 1, We will be hit by divide by 0

Previous car lease example:

lua> n,pv,pmt,fv = 36,30000,-550,-15000
lua> -(pv+fv)/(pv-fv) -- within +/- 1
-0.3333333333333333
lua> pmt/fv, -pmt/pv -- t=-1 and t=1 edges, both same sign.
0.03666666666666667      0.018333333333333333

At t=0, x = -pmt / (A/0 + B) = -pmt/∞ = 0

Thus, we have 2 ranges: (x > pmt/fv) || (x < -pmt/pv)

From tanh info, rate gap, pmt/fv .. -pmt/pv, is not possible, *opposite* of OP claim.