20. You have estimated spot rates as follows:

r 1 ⫽ 5.00%, r 2 ⫽ 5.40%, r 3 ⫽ 5.70%, r 4 ⫽ 5.90%, r 5 ⫽ 6.00%.

a. What are the discount factors for each date (that is, the present value of $1 paid in year t )?

b. Calculate the PV of the following bonds assuming annual coupons: (i) 5%, two-year bond; (ii) 5%, five-year bond; and (iii) 10%, five-year bond.

c. Explain intuitively why the yield to maturity on the 10% bond is less than that on the 5% bond.

d. What should be the yield to maturity on a five-year zero-coupon bond?

e. Show that the correct yield to maturity on a five-year annuity is 5.75%.

f. Explain intuitively why the yield on the five-year bonds described in part

(c) must lie between the yield on a five-year zero-coupon bond and a five-year annuity.