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Assignment 2 Solution

# Assignment 2 Solution - Econ 500 Fall 2011 Z Janko...

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1 DEPARTMENT OF ECONOMICS Econ 500 – Money and Banking Fall 2011 Assignment 2 – Answer Key 1. Chapter 4, Q8 from textbook: To pay for college, you have just taken out a \$1000 government loan that makes you pay \$126 per year for 25 years. However, you do not have to start making payments until you graduate from college TWO years from today . Why is the yield to maturity (TODAY) necessarily LESS than 12%? (Hint: remember that the yield to maturity (TODAY) is exactly 12% on a normal (standard) \$1000 fixed payment loan, in which you pay \$126 per year for 25years starting next year). Recall, that if the PV of X = Y, then X>Y; and the further the future payment, the bigger the difference between X and Y, for a given interest rate. (Just look at question 5)! Hence, if the Loan to be repaid is \$1000, and the payments are \$126, the further the payment is in the future (given i=10%) the lower the PV of that future payments. Hence, if the payments are postponed, then the PV (i.e. the sum of all those payments) of the loan is going to be smaller for i=10%, and will not equal \$1000. In that case, i has to fall in order for the PV to increase to \$1000. So, i is smaller than \$1000. Another Way to see the answer to Question 7 is (a bit long) but hopefully clear: Suppose you did start to pay next year. Then the PV is (1) 2 25 FP FP FP PV .... (1 i) (1 i) (1 i) Get yield to maturity by setting PV=LV 2 25 126 126 126 1000 .... (1 i) (1 i) (1 i) From chapter 4 (text) we know that in this case i = 12%. Now if I start paying 2 years from now not 1 year from now the PV is Econ 500 Fall 2011 Z. Janko

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2 (2) 2 3 26 126 126 126 PV .... (1 i) (1 i) (1 i) note that n = years to maturity is still 25 NOW LETS COMPARE THE PRESENT VALUE IN EQUATION 1 AND THE PRESENT VALUE IN EQUATION 2 2 25 126 126 126 PV1 .... (1 i) (1 i) (1 i) 2 3 25 26 126 126 126 126 PV2 .... (1 i) (1 i) (1 i) 1 i The difference between the two is : PV1 has 126 (1 i) but does not have 26 126 (1 i) PV2 has 26 126 (1 i) but does not have 126 (1 i) Question: If i=12% which term is bigger: 126 (1 i) or 26 126 (1 i) ?
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Assignment 2 Solution - Econ 500 Fall 2011 Z Janko...

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