2. A financial analyst wants to estimate the modified duration and convexity of a 30-year 4% bond trading at par, using numerical approximation. Follow her steps below to compute the modified duration and convexity of this bond (assuming the bond pays coupons annually). (20 points) a) Calculate the bond price if yield-to-maturity goes UP and goes DOWN by 10 basis point. b) Using numerical approximation, estimate the modified duration of this bond. c) Using numerical approximation, estimate the convexity of this bond.