. Consider two bonds A and B with payments , where = 1,2, ,10. Both bonds have $1,000 face value. Bond A has just been issued, it bears coupon rate of 7%, and it will mature in 10 years. Bond B was issued 5 years ago, when interest rates were higher. This bond has $1,000 face value and bears a 13% coupon rate. When issued, this bond had a 15-year maturity, so its remaining maturity is 10 years. The yield to maturity is 7% (see Cell B2). Using the Excel spreadsheet below, estimate the duration of each of the two bonds A (Cell B20) and B (Cell E20), using the mathematical formula of the Macaulay duration measure. Which bond has the longest duration? Show your calculations and interpret your results.

B G H ! D BOND DURATION CALCULATION Yield to Maturity (YTM) 7% Time-Weighted Average Maturity of the Payments Received From the Bond A Time-Weighted Average Maturity of the Payments Received From the Bond B 4 Year CA 5 1 130 6 7 8 9 10 11 2 3 4 5 6 7 70 70 70 70 70 20 70 0.0654 0.1223 0.1714 0.2136 0.2495 0.2799 0.3051 130 130 130 130 130 130 0.0855 0.1598 0.2240 0.2791 0.3260 0.3657 0.3987 130 12 13 14 15 16 70 70 1,070 0.3259 0.3427 5.4393 130 0.4258 0.4477 4.0413 10 1.130 17 Bond price 1,000.00 1,421.41 18 19 Estimation of the Macaulay duration using the mathematical formula 20 Duration ? ? 21 Question e