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##### (Solution) - A relative sends you a U S government savings bond that

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A relative sends you a U.S. government savings bond that matures in n years with a face value of \$100. This means that the holder of this bond is entitled to collect \$100 from the government n years from now.
A: Suppose the interest rate is 10%.
(a) If n = 1, how much current consumption could this bond finance and how much do you therefore think you could sell this bond for today?
(b) Does the bond become more or less valuable if the interest rate falls to 5%?
(c) Now suppose that n = 2. How valuable is the bond if the interest rate is 10%?
(d)What if n = 10?
B: Consider a bond that matures n years from now with face value x when the expected annual interest rate over this period is equal to r.
(a) Derive the general formula for calculating the current consumption that could be financed with this bond.
(b) Use a derivative to show what happens to the value of a bond as x changes.
(c) Show similarly what happens to the value as r changes. Can you come to a general conclusion from this about the relationship between the interest rate and the price of bonds?

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