A bond with a yield to maturity of 3% and a coupon rate of 3% has 20 years remaining until maturity. Using the approximate formula (for long term bonds) calculate the duration and the modified duration for this bond assuming annual interest payments and a par value of $1,000. Why is the duration of this bond higher than the 20-year 10% coupon bond yielding 10% we looked at in class that had a duration of 9.4 years? If the required market yield on this bond increases to 4%, what approximate per cent change in the bond price would you have based on the modified duration?