Solving the TVM equation for the interest rate

[ttw]

I used to have a continued fraction approximation for interest rate (from an old finance book whose title I no longer remember.) It was quite accurate over a very wide range of initial conditions. I'll see if I can find it. (None of the newer texts had this formula.) I'll try the Internet Archive to see if I can find the book.

One method we used to use was to figure out the rate assuming simple interest then adjust by some factor (like dividing by 1.5 or 2.0). This made a pretty good starting point. There are input values which do not have a real solution for the interest rate though. One could also replace Newton's method with something more robust like the secant or even binary interval halving for the first few steps.