2. Duration (25 points) You observe the following prices of zero coupon bonds (assume that they have face value 100). Please use annual discounting throughout this question. Maturity: Bond price: 2 99.68 7 96.43 20 76.48 a. What are the 2, 7, and 20-year spot rates (yields to maturity on zero coupon bonds)? b. What are the Macaulay durations and modified durations for each of the three bonds? (Please provide six numbers.) c. Imagine that tomorrow spot rates increase by 0.5% for all maturities. What are the predicted percentage price changes for the three bonds? Which bond's price changes by the most