The duration is the sum of the year × fraction of total value row, or 6.395 years. The modified duration, or volatility, is 6.395 / (1 + .04) = 6.15.The price of the 3 percent coupon bond at 3.5 percent, and 4.5 percent equals $969.43 and $911.61, respectively. The price difference is $57.82, or 6.15 percent of the bond’s value at the 4 percent discount rate. The percentage difference is equal to the 1 percent change in the discount rate × modified duration.