20.Spot interest rates and yields 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.