An investor is considering the purchase of zero-coupon bonds with maturities of one, three, or five years. Currently the spot rates for 1-, 2-, 3-, 4-, and 5-year zero-coupon bonds are, respectively, 0.031, 0.035, 0.04, 0.042, and 0.043 per year with semi-annual compounding. A financial analyst has advised this investor that interest rates will increase during the next year and the analyst expects all spot rates to increase by the amount 0.005, so that the one-year spot rate will become 0.03, and so forth. The investor plans to sell the bond at the end of one year and wants the greatest return for the year. Part A Numerical (a) What are the current prices of 1-, 3-, and 5-year zero-coupon bonds with par values of $1000? (b) What will be the prices of these bonds one year from now if spot rates remain unchanged? (c) What will be the prices of these bonds one year from now if spot rates each increase by 0.005? (d) If the analyst is correct that spot rates will increase by 0.005 in one year, which maturity, 1, 3, or 5 years, will give the investor the greatest return when the bond is sold after one year? Justify your answer.

(e) If instead the analyst is incorrect and spot rates remain unchanged, then which maturity, 1, 3, or 5 years, earns the highest return when the bond is sold after one year? Justify your answer. (f) The analyst also said that if the spot rates remain unchanged, then the bond with the highest spot rate will earn the greatest one-year return. Is this correct? Why? (Hint: This problem does the bond math to see which maturity, 1, 3, or 5 years, will give the best return under two scenarios: interest rates are unchanged and interest rates increase as forecast by the analyst. Be aware that a bond will not have the same maturity in one year as it has now, so the spot rate that applies to that bond will change.)

Only Part E and F.