MATH 2FM3 Lecture Notes - Lecture 8: Discounting
22 Oct 2015
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2. 1. 2 present value of an annuity: example: you want to open a saving account with a single deposit today so that you can withdraw 1000 per year for 4 years, starting 1 year from now. Find the amount you have to deposit if i = 6% with annual compounding: solution: let x be the amount you deposit. X(1. 06) 1000, after 2nd withdrawal the balance is. [x(1. 06) 1000](1. 06) 1000 = x(1. 06)2 1000(1. 06) 1000, after 3rd withdrawal the balance is. 0 and after 4th withdrawal the balance is. X(1. 06)4 1000(1. 06)3 1000(1. 06)2 1000(1. 06) 1000. Setting the 4th withdrawal to 0, we get. X(1. 06)4 = 1000(1. 06)3 + 1000(1. 06)2 + 1000(1. 06) + 1000, or. X = 1000[ + 2 + 3 + 4] = 3, 465. 11, where = 1. 1+i is the present-value factor: we can generalize this example for n withdrawals to get. X = 1000[ + 2 + + n] = 1000 1 n.
