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midterm01_solns

# midterm01_solns - UGBA 103 2010 Midterm Solutions 1(a 10K...

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UGBA 103 2010 Midterm Solutions 1. (a) 10 K today: PV (11 K ) = 11 K 1 . 025 5 = 9722 . 40 < 10 K (b) 1 + r nom = (1 + i )(1 + r real ) r real = 1 . 1 / 1 . 05 - 1 = 4 . 7619% 2. The mortgage has 17 years left, so there are N = 17 * 12 = 204 payments of C = 1500 remaining. The effective monthly interest rate r m = APR/ 12 = 9% / 12 = 0 . 75%, so the mortgage balance is Balance = C r m bracketleftbigg 1 - 1 (1 + r m ) N bracketrightbigg = 1500 0 . 0075 bracketleftbigg 1 - 1 1 . 0075 204 bracketrightbigg = 156 , 444 . 92 3. Note that we are interested exclusively in real cash flows: the desired retirement savings as well as Mr. T’s salary growth are given in real terms. So we can simply value the real savings plan at using the real discount rate. There are actually two ways to interpret the question: a) the salary of 60 K received at t = 1 is already in real terms (this is the intended interpretation); b) the salary of 60 K is in nominal terms, so we need to deflate it one period to 60 K/ 1 . 03 = 58252 . 43 to get it in real terms. If the fraction of income saved is x , then in each case we want: (a) PV (savings) = PV (retirement goal) x 60 , 000 0 . 06 - 0 . 05 bracketleftBigg

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midterm01_solns - UGBA 103 2010 Midterm Solutions 1(a 10K...

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