14. An investor is considering the purchase of zero-coupon bonds with maturities of one, three, or 5 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 semiannual 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 1-year spot rate will become 0.036, and so forth. The investor plans to sell the bond at the end of 1 year and wants the greatest return for the year. 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.

(a) What are the current prices of 1-, 3-, and 5-year zero-coupon bonds with par values of $1,000?

(b) What will be the prices of these bonds 1 year from now if spot rates remain unchanged?

(c) What will be the prices of these bonds 1 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 1 year, which maturity, 1, 3, or 5 years, will give the investor the greatest return when the bond is sold after 1 year? Justify your answer.