2. You purchased a bond with $1000 face value, 2 years maturity, 10% coupon rate (coupon payments are made semiannually). Your required rate of return is 8%. (8 points) a. Calculate the price of the bond. When interest rate decreases by 1%, how does the price of the bond change? Calculate the price elasticity of the bond. b. Calculate the duration and modified duration of the bond. Use the modified duration to estimate the percentage change in bond price if interest rate falls by 1%. Compare it with the answer in part a)