4. (25 points) A bond has 2 years to maturity. The coupon rate is 0% and the market rate of interest is 6%. Face value is M = 1000 a. Find the duration for the bond. (10 points) b. If the market rate of interest changes to 7%, estimate the change in the price of the bond using duration. (4 points) c. Calculate the actual change in the price of the bond by computing the new price. (4 points) d. Why does the expected change in bond price differ from the actual? (4 points) e. If the coupon rate was greater than zero, what would happen to the duration? (3 points)