Mathematics of Asynchronous Annuities

Asynchronous annuities are defined as those in which the frequency of cash flows differs from the frequency of interest compounding. The conventional approach to calculating the present and future values of such annuities is to impute a rate of interest (or return) to a cash flow period, which is then inserted into standard annuity equations. The method produces inaccurate results when the frequency of cash flows exceeds the frequency of interest compounding. After identifying the source of those inaccuracies, this paper develops and demonstrates a new approach to accurately solving annuity problems when the frequency of cash flows exceeds the frequency of interest compounding.