Suppose the yield to maturity on a 6.5% coupon bond is 4.5%. The bond has a face value of $1,000, pays coupons semi-annually, and has a Macaulay duration of 11.22 years. Its price is 1,235.90. What is this bonds modified duration?

Now suppose the yield to maturity on this bond decreases to 3.5%. Approximately what will be the percentage increase in the bonds price? Approximately what will the new price of the bond be? (Its actual new price would be $1,381.90).

What is the source of the error in this estimate?