You have estimated spot rates as follows: = = 6.00%. 11 = 5.00%, 12 = 5.40%, 13 = 5.70%, 14 5.90%, 15 = 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.