Calculates an internal rate of return that converts the payment stream into
the present value.  It is an iterative function, meaning it tries successive
guesses until an interest rate works.

From the Help file

Returns the interest rate per period of an annuity. RATE is calculated by
iteration and can have zero or more solutions. If the successive results of
RATE do not converge to within 0.0000001 after 20 iterations, RATE returns
the #NUM! error value.

RDph <R...@discussions.microsoft.com> wrote...

It almost certainly uses a Newton-Raphson iterative approach since
it's easy to calculate the necessary derivatives. Every numerical
programming text I've seen covers solving polynomials in one variable
using that algorithm.