Suppose that the forward rate is r(t)= XXXXXXXXXX0002t − 0.00003t 2 . a) What is the yield to maturity of a bond maturing in 8 years?  (b) What is the price of a par $1,000 zero-coupon bond maturing...

Suppose that the forward rate is r(t)=0.04 + 0.0002t − 0.00003t².

a) What is the yield to maturity of a bond maturing in 8 years?

 (b) What is the price of a par $1,000 zero-coupon bond maturing in 5 years?

 (c) Plot the forward rate and the yield curve. Describe the two curves. Which are convex and which are concave? How do they differ?

 (d) Suppose you buy a 10-year zero-coupon bond and sell it after 1 year. What will be the return if the forward rate does not change during that year?