10.) A bond has a $1,000 face value and 10 years to maturity. It has a 7% coupon (paid semiannually). This bond has a modified duration of 6.9 years.

Initially, the yield to maturity on the bond is also 7% and the bond sells for par value.

The Federal Reserve cuts interest rates instantaneously and the yield to maturity on this bond falls to 5%.

a.) Using the modified duration statistic above, what is the predicted percentage change in this price of this bond when the yield to maturity decreases from 7% to 5%?

b.) Compute the exact percentage change in the price of this bond when the yield to maturity decreases from 7% to 5%.

c.) Briefly explain why your answers in parts a.) and b.) above are not exactly equal.