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Unformatted text preview: Math 006 (Lecture 4) Present Value of an Annuity Example 1. How much should you deposit in an account paying 6% compounded semi- annually in order to be able to withdraw $1000 every 6 months for the next 3 years? (After the last payment is made, no money is to be left in the account) In general, if R is the periodic payment, i is the interest rate per period, and, n is the number of periods, then the present value of all payments is given by S = R (1 + i )- 1 + R (1 + i )- 2 + · · · + R (1 + i )- n . 1 We now introduce the formula of the present value of an annuity in the term of the notations used in finance. Theorem 1. Let PV = present value of all payments, PMT = periodic payment, i = interest rate per period and n = number of payments. We have PV = PMT 1- (1 + i )- n i = PMTa n e i where a n e i = 1- (1 + i )- n i . Example 2. Recently Lion bank offered an ordinary annuity that earned 5% compounded annually. A person plans to make equal annual deposits into this account for 30 years inannually....
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This note was uploaded on 09/04/2010 for the course MATH MATH006 taught by Professor Forgot during the Fall '09 term at HKUST.
- Fall '09