(02-12-2020 05:25 PM)Albert Chan Wrote: This formula is based on Pade[1,1], I centered 0, of NFV = F + P + ((1+I)^N-1)*(P+M/I)

Solving Pade[1,1] approximated NFV = 0, for 1/I :

\( \Large {1\over I} ≈

{\binom{N}{3}M + \binom{N}{2}P \over \binom{N}{2}M + \binom{N}{1}P} -

{\binom{N}{2}M + \binom{N}{1}P \over F + P + M N}\)

Doing the same example, N=11, F=40000, P=0, M=-2564

1/I ≈ (-423060/-141020) - (-141020/11796) = 44102/2949

I ≈ 2949/44102 ≈ 6.687%, which under-estimated true rate (6.780%) by tiny 0.093%

One could use this formula as an initial approximation to Newton's method or something else. A good initial approximation is necessary for all iterations and the your [1,1] Pade looks really good.