You find a bond with 19 years until maturity that has a coupon rate of 8% and a yield to maturity of 7%. What is the Macaulay duration? The modified duration? Moreover, suppose the yield to maturity is increased by 0.25%. What is the new price of the bond using duration? What is the new price of the bond using the bond pricing formula? What if the yield to maturity increase by 1%? By 2%? by 5%? What does this tell you about using duration to estimate bond price changes for large interest rate changes?