Polynomial Annuities

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 pr...

Full description

Saved in:
Bibliographic Details
Published in:AppliedMath 2022-06, Vol.2 (2), p.212-233
Main Authors: Rajaram, Rajeev, Ritchey, Nathan
Format: Article
Language:English
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 {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.
ISSN:2673-9909
2673-9909
DOI:10.3390/appliedmath2020013