Mathematics of complex annuities
Chris Deeley
Working Paper No. 15/07
December 2007
About the Author
- Chris Deeley
School of Accounting and Computer Science
Charles Sturt University
Charles Sturt University – Faculty of Business Working Paper Series
Managing Editor: Associate Professor Jayne Bisman, School of Accounting, Bathurst
Editors: Dr P. Mathews, School of Commerce, Wagga Wagga
Associate Professor M. O'Mullane, School of Business, Albury
Dr R. Tierney, School of Marketing and Management, Bathurst
Dr D Ardagh, School of Commerce, Wagga Wagga
Ms K Mather, School of Computing and Mathematics, Wagga Wagga
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Abstract
Complex annuities are defined as those in which the frequency of cash flows differs from the frequency of interest compounding. The conventional approach to solving complex annuity problems is to match the frequency of interest compounding with the frequency of cash flows by imputing a rate of interest per cash flow period. Complex annuities are thereby transformed into simple annuities, measured in cash flow periods, and so brought within the solution framework of standard annuity equations. However, 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.
Keywords: complex annuities
JEL code: G300