Spot interest rates and yields You have estimated spot rates as follows:

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 and face values of $1,000: 

• 5%, two-year bond; 
• 5%, five-year bond;  
• 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. 

r=5.00%, r = 5.40%, r3 = 5.70%, r4 = 5.90%, r5 = 6.00%.