Problem 4 (10 points) Consider a bond with $1000 face value and 8% coupon rate with interest paid on an annual basis. The bond has 5 years to maturity and yield-to-maturity (YTM) of 10%. Label this YTM as y. A. Find the current price of the bond and label it as P1. Also calculate the Duration (D) and Convexity (C) of the bond. B. Now assume the YTM increases from 10% to 10.1%. Find the price of the bond at the new YTM. Label the new YTM and price as y2 and P2, respectively. C. Calculate the relative changes in the price of the bond and the YTM as follows: . = P2 - P1 P1 and 1+ y = Y2 Vi 1 + y Ay D. Use the Duration (D) calculated in step (A) to calculate -D X Is your answer 1+y AP reasonably close (say, 2 decimal places after converting to percentages) to calculated in step (C)? In instances when the two estimates are not close, what would you also have to consider? that you P