Polynomial Annuities

Rajeev Rajaram, Nathan Ritchey
2022 AppliedMath  
We use a payment pattern of the type {1k,2k,3k,...} to generalize the standard level payment and increasing annuity to polynomial payment patterns. We derive explicit formulas for the present value of an n-year polynomial annuity, the present value of an m-monthly n-year polynomial annuity, and the present value of an n-year continuous polynomial annuity. We also use the idea to extend the annuities to payment patterns derived from analytic functions, as well as to payment patterns of the type
more » ... 1r,2r,3r,...}, with r being an arbitrary real number. In the process, we develop possible approximations to k! and for the gamma function evaluated at real numbers.
doi:10.3390/appliedmath2020013 fatcat:sbfnt57kjrer5i4ereqfhgrufy