Narrow Bounds for the Effective Rate of Return Concerning a Special Problem for Annuities

We consider the calculation of the effective rate of an annuity which was derived by changing the conditions of a given annuity in a certain manner. In this note we will derive narrow bounds for the effective rate of the changed annuity in terms of the (given) rate of the original annuity and the coefficients of the polynomial involved. It is demonstrated by some numerical examples that the bounds achieved for this purpose are of sufficient accuracy for practical applications and thus an application of an iterative method for solving the equation can be avoided.