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Lecture 9

Actuarial Science 2053 Lecture 9: Sep 30, 2015

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Western University
Actuarial Science
Actuarial Science 2053
Steven Kopp

Equivalent Rates (section 2.2) Recall j = nominal rate of interest, m compounded mtimes a year i = interest rate per period We now define: j = annual effective rate of interest t h a t i s e q u i v a l e n t t o j m Meaning of Equivalent Interest Rates If j and j are equivalent rates of interest, m they must produce the same amount of interest over a oneyear period (Actually, they must produced he same amount of interest over any period of time) OR They must produce the same accumulated values over any period of time. Relationship To develop a relationship between j and j, m lets accumulate 1 for one year under both interest rates Investing at j, 1 will accumulate to (1 + j) at the end of 1year Investing at j, 1 will accumulate to m j m m (1 + ) at the end of 1year m
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