15. The duration of an II-year, $1,000 Treasury bond paying a 10 percent semiannual coupon and selling at par has been estimated at 6.9 years. a. What is the modified duration of the bond? Modified Duration = D/(l + R/2) = 6.9/(1 + .10/2) = 6.57 years b. What will be the estimated price change on the bond if interest rates increase 0.10 percent (10 basis points)? If rates decrease 0.20 percent (20 basis points)? Estimated change in price = -MDx AR x P = -6.57 x 0.001 x $1,000 = -$6.57. Estimated change in price = -MDx AR x P = -6.57 x -0.002 x $1,000 = $13.14. c. What would be the actual price of the bond under each rate change situation in part (b) using the traditional present value bond pricing techniques? What is the amount of error in each case? Rate Change + 0.001 - 0.002 Price Estimated $993.43 $1,013.14 Actual price $993.45 $1,013.28 Error $0.02 -$0.14