You must show all work for full credit. Problem 1 (20 points) Suppose you have the following obligation over the next three years. In years 1 and 2, you will make payments $5,000 and in year 3 , you must make a payment of $10,000. Interest rates are currently 5%. Part a: What is the duration of your obligation? Part b: Two zero coupon bonds exist. Bond A has a time to maturity of 1 year and bond B has a time to maturity of 3 years. Explain how you would immunize against your obligation? Part c: Assuming an interest rate of 5%, what is the face value of Bond A and what is the face value of B ond B ? Part d : Show that if interest rates increase to 6%, the present value of your obligation will be offset by the present value of your bond portfolio