1. (Assume an annual payment timing convention for this question). Borrowing and lending occur 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.
   1. What is the zero-coupon rate between now and two years from now?
   2. What is the zero-coupon rate between now and three years from now?
   3. What coupon rate would a 2-year bond have to be priced at par?
   4. What coupon rate would a 3-year bond have to be priced at par?
   5. What are the Macaulay and modified durations of the 3-year coupon-paying bond in d) above?
   6. What are the Macaulay and modified durations of a 3-year zero-coupon bond?
   7. 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 the dollar duration of each position was the same. What is a scenario (related to changes in yields) in which you would lose money?