Borrowing and lending occurs at the same rates, and there are no taxes and there is no credit risk. The interest rate between now and one year from now is 5 percent per year, the forward rate between one year from now and two years from now is 7 percent per year, and the forward rate between two years and three years from now is 9 percent per year. (50 points total) spot rate a. What is the zero-coupon rate between now and two years from now? (5 points) b. What is the zero-coupon rate between now and three years from now? (5 points) c. What coupon rate would a 2-year bond have to have in order to be priced at par? (5 points) d. What coupon rate would a 3-year bond have to have in order to be priced at par? (5 points) e. What are the Macaulay and modified durations of the 3-year coupon-paying bond in d) above? (10 points) f. What are the Macaulay and modified durations of a 3-year zero-coupon bond? (10 points) g. Suppose that you purchased the 3-year coupon-paying bond and took a short position in the 3-year zero-coupon bond in quantities such that dollar duration of each position was