A financial portfolio consists of two bonds, with the following characteristics: Bond Price Mod Mod A B 4,742.3 463. 2 2.619 9.507 9.25994.307 Bond A matures in 3 years and pays annual coupons at rate 6%. Both the par value and the redemption value are $5,000. Bond B is a zero-coupon bond that matures for $1,000 in 10 years. The effective annual yield rate of each bond is 8%. (a) Demonstrate that the modified duration of Bond A is 2.619. (b) Demonstrate that the modified convexity of Bond B is 94.307. (c) Determine the modified duration and the modified convexity of the portfolio at an 8% effective annual interest rate. (d) Use the second-order modified approximation to estimate the market value / price of the portfolio if the interest rate decreases suddenly to 7%. (e) Redo part (d) using the first-order Macaulay approximation