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Unformatted text preview: Math 006 (Lecture 3) Future Value of an Annuity Definition 1. An annuity is a sequence of equal periodic payments. We call it an ordi- nary annuity if the payments are made at the end if each time interval. The amount, or future value , of an annuity is the sum of all payment plus all interest earned. Example 1. Suppose you deposit $100 every 6 months into an account that pay 6% compounded semiannually. If you make six deposits, one at the end of each interest payment period, over 3 years, how much money will be in the account after the last deposit is made? In general, if R is the periodic deposit, i is the interest rate per period, and, n is the number of periods, then the future value is given by S = R + R (1 + i ) + R (1 + i ) 2 + + R (1 + i ) n- 1 . 1 We now introduce the formula of the future value of an annuity in the term of the notations used in finance. Theorem 1. Let FV = future value, PMT = periodic payment, i = interest rate per period and n = number of payments. We havenumber of payments....
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- Fall '09