Estimating the Rate of Interest For An Ordinary Annuity Certain
Eugen Ionascu and Richard Stephens
ABSTRACT
Textbooks on the Theory of Interest (Kellison) and study guides for Exam FM/2 (Finan)
offer approximations of the effective interest rate for an ordinary annuity when the present value
or future value is known. These approximations are poor. When the present value is fixed, the
standard approximation approaches 2𝑖 as 𝑛 becomes large. Although the future value can not be
fixed for all 𝑛, the standard approximation approaches zero as 𝑛 becomes large.
An accurate estimate (Silver) is known when the present value is known. We improve
this estimate and analyze the case when the future value is known.
References:
Donald, D. W. A. Compound Interest and Annuities-Certain (The Cambridge University Press,
1953)
Finan, Marcel B. A Basic Course in the Theory of Interest and Derivatives Markets: A
Preparation for the Actuarial Exam FM/2 (Arkansas Tech University, 2012)
Kellison, Stephen G. The Theory of Interest (McGraw-Hill/Irwin, 3rd Edition, 2009)
Silver, Murray. An Approximate Solution for the Unknown Rate of Interest: For An Annuity
Certain (The Journal of Risk and Insurance, Vol. 28, No. 1, 1981, pp. 136-142)
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