4. (35 points) You are given the following data for a bond. The Coupon Payment is $50 on a 5-year bond (5 years until maturity) with a Face Value of $1000. The current interest rate (YTM) is 10%. Fill in the following table. Year Cash Flow (CF) Present Value (PV) Weight 1 2 3 4 S 5 a. Determine the Price of this bond. Weighted Maturity DUR= b. Determine the (Macaulay) Duration for this bond (FOR FULL CREDIT SHOW YOUR WORK FOR PERIODS 3 AND 4: DERIVE THE WEIGHT AND WEIGHTED MATURITY): CF CF DUR (+11)-((1+1) = CF 21+ (1+1) P. c. Determine the Modified Duration for this bond. Price of Bond 810.46 Duration 4.49 years. Modified Duration = 4.08% d. (FILL IN THE TABLE BELOW) Calculate the APPROXIMATE new price of the bond using your measure of modified duration and the percentage change in the price of the bond for the following interest rates (Columns 2 and 3). Calculate the exact new price of the bond (above) and the exact percentage change in the price of the bond for the following interest rates (Columns 4 and 5). %AP = -MDAL Pt+1 = (1+ MDI)P-MDP+1 FV PN C == c [ ( 1 ( 1 + 1)")] + a = (1-(+)")]+a+* YTM 1+1 New Price Pt+1 (Approx) Percentage Change in the Price %AP (Approx) New Price Pt+1 (Actual) Percentage Change in the Price %AP (Actual) 0.04 0.06 0.08 0.10 0.12 0.14 0.16. SHOW YOUR CALCUATIONS FOR INTEREST RATES 0.8 AND 0.12 FOR FULL CREDIT.