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.

(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?