Generalized Multiple Economy Cost-of-Living Ordinary Annuities From an Interest Theory Perspective

The comprehensive development and application of progressive levels of generalization of the concept of a classic ordinary annuity from an interest theory perspective with either discrete or continuous compounding (first level) is the focus of this article. The second level incorporates the effect of inflation, or cost-of-living, on the annuity rent specified by a second interest rate. Next, we allow the principal to fund multiple investment economies, each with its own cost-of-living interest rate (third level). The fourth level recognizes the need for different payment spans and nonuniform economy-dependent annuity rents and its utility is illustrated with a multinational corporation capital investment example. At the fifth level, cost-of-living interest rates are allowed to vary over time. A retirement example illustrates application of the most generalized annuity formula derived. Finally, useful tables presented throughout the article summarize a total of 29 annuity formulas.

ACKNOWLEDGMENTS

The authors acknowledge funding from a University of St. Thomas faculty partnership grant (FPG) in addition to a nontenured faculty grant for the second author from the 3M Corporation of Maplewood, MN.

Notes

¹ (r ₁ ^N + r ₁ ^N-1 r ₂ + ··· + r ₁ r ₂ ^N-1 + r ₂ ^N = (r ₁ ^N+1 - r ₂ ^N+1)/(r ₁ - r ₂) provided r ₁ ≠ r ₂.

Additional information

Notes on contributors

Michael P. Hennessey

Affiliated with St. Thomas' Center for Applied Mathematics (CAM).