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Unformatted text preview: EC314Fall 2008 Solutions – Problem Set 2 Matt Turner (updated: 24 September 2008) . 1. Prove that ∑ ∞ t = 1 ( 1 1 + r ) t = 1 r . n ∑ t = 1 1 1 + r t = 1 1 + r + ... + 1 1 + r n 1 1 + r n ∑ t = 1 1 1 + r t = 1 1 + r 2 + ... + 1 1 + r n + 1 Subtracting the second equation from the first gives 1 1 1 + r n ∑ t = 1 1 1 + r t = 1 1 + r 1 1 + r n + 1 Simplifying gives n ∑ t = 1 1 1 + r t = 1 + r r " 1 1 + r 1 1 + r n + 1 # = 1 r 1 r 1 1 + r n = 1 r 1 r 1 1 + r n Taking a limit gives us the result. ∞ ∑ t = 1 1 1 + r t = lim n → ∞ n ∑ t = 1 1 1 + r t = 1 r 2. One problem with discounting is that is counts future benefits very little after we get more than a few years ahead. To see this, conduct the following three exercises: a. Write the expression for the present value of a one hundred dollar payoff 100 years from now as a function of the interest rate. b. Plot this present value as a function of r ....
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This note was uploaded on 01/27/2009 for the course ECO 314 taught by Professor Matthewturner during the Winter '08 term at University of Toronto Toronto.
 Winter '08
 MATTHEWTURNER

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