You have estimated spot rates as follows:
r1 = 5.00%, r2 = 5.40%, r3 = 5.70%, r4 = 5.90%, r5 = 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.
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