Iterative solution of the interest rate in a financial transaction: the hyperbolic method

Extract

1.1 This note describes an iterative method for determining the root of an equation, based on the assumption that the curve representing the equation is a rectangular hyperbola near the root.

1.2. The method was derived for use in calculating the interest rate under financial contracts. Despite having a theoretically slower rate of convergence than Newton's method, in practice the hyperbolic method seems to require a fewer number of iterations for comparable accuracy. Moreover, it applies where the form of the function being evaluated is incapable of explicit description, and hence its derivative cannot be defined, such as where reinvestment rates of return are assumed.