Request TVM formula guidance

[iMatt04bit]

I found an improvement for the Secant method where it will solve much faster:

Code:

x0 = x0 - fx0 * ((x0 - x1)/(fx0 - fx1));

This should follow the other line with similar code.
Now the secant method decrements from both x0 and x1 points as it solves.

I have run some preliminary tests using a variety of TVM scenarios with good results.
Min/max number of iterations to solve for 21 scenarios tested are:
Newton: 2,6 and Secant: 5,9
The Newton method appears to offer the best accuracy.

I left out the stats for the double root scenarios because I am still looking for a formulaic method for determining:
1) a double root exists 2) an approximation of the 2nd root value - with an indication of sign.

I used the Euler methods (thanks Dieter) which have shown improved results.
A code sample:

Code:

f1 = Math.exp(N * Math.log1p(R));  // (1+R)^N
f2 = Math.exp(-N * Math.log1p(R));         // (1+R)^-N
f3 = Math.exp( (-N-1) * Math.log1p(R));  // (1+R)^(-N-1)

I attached 2 files for anyone interested.
The pdf file shows a comparison of values between emu-calculators and both solver methods. And the text file shows the output giving an indication of how well the methods are solving.