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Unformatted text preview: Perpetuities (section 4.3) A perpetuity is an annuity where the payments begin on a fixed date and continue forever • since payments continue forever, it is meaningless to calculate accumulated values • we will only look at the present value of perpetuities Real Life Examples of Perpetuities Example Consider a person who invests $1000 today in a fund earning j 4 = 8% • she earns 1000 x 0.02 = $20 of interest at the end of 3 months • if she withdraws this interest, she will have $1000 left in the fund • this $1000 will earn another $20 of interest in 3 months • if she withdraws this interest, she will have $1000 left over and she will earn another $20 of interest • ….and so on Thus, 1. If the interest rate does not change and 2. The original principal of $1000 is kept intact, Then interest payments of $20 can withdrawn forever In General 1. Ordinary Simple Perpetuity R = Ai ⇒ A = i R 2. Simple Perpetuity Due A = R + i R Example 4.3.1 How much money is needed today to establish a scholarship fund paying $1500 annually at j 1 = 8%, if the first scholarship is to be paid: (a) one year from now (b) today (c) 5 years from now (d) 1 year from now, but with interest at j 4 = 8% (e) If you had $20,000, what size annual scholarship could you offer, 1st scholarship to be paid year from now? Solution to 4.3.1 Annuities Where Payments Vary (section 4.4) Not all annuities have a level series of payments; instead we are going to look at annuities where the payments change...
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This note was uploaded on 04/14/2010 for the course ACSCI 2053 taught by Professor Kopp during the Spring '09 term at UWO.
 Spring '09
 Kopp

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