I can’t quite understand can we calibrate a binominal tree without excel? If we have estimated f(1,1), f(2,1) etc. and the volatility is given, can we build the binominal tree without Solver? If not, why?

My logic is as follows: at t=1 if I have estimated f(1,1):

i(1,high) shall be equal to f(1,1) multiplied by e power sigma;

i(1,low) shall be equal to f(1,1) multiplied by e power minus sigma

At t=2 for estimated f(2,1):

i(2, high, low) = f(2,1)

i(2, high,high) = f(2,1) multiplied by e power 2*sigma

i(2, low, low) = f(2,1) multiplied by e power -2*sigma etc.

When I try to build a binominal tree in such a way however I’m not achieving the interest rate tree that is given by CFAI / Wiley. I haven’t found in Reading 43 where I’m wrong. Any idea?