41C/CV root finders

[Ángel Martin]

(05-20-2015 07:07 PM)Dave Britten Wrote:  Does anybody have any recommendations for good root finders, or techniques for obtaining initial guesses for i%?

Here's the formula I used in the TVM Module for the first derivative (as it uses Newton's method):

f ’ (i) = (PMT / i^2 ) * [ (1+i)^(-n) - 1 ] + n * [PMT (1 + ip)/i – FV ] * (1+i)^-(n+1)

with initial value:
i0 = [ abs( PV + n*PMT + FV) ]^1/n

Seems to hold up quite well but again this is a MCODE implementation using the internal 13-digit precision routines from the OS.

Note: edited to add the missing exponent signs.


Cheers,
AM