8. You have purchased a bond with 4 years to maturity (face value $1,000), paying a coupon rate of 6.5% (paid annually), trading at a yield to maturity of 7.4%. a. What is the bond's Macaulay duration? b. You expect that yields will fall by 0.3%. Use the modified duration to find the approximate percentage change in the price of the bond. C. What is the actual new price of the bond at its new yield-to-maturity? (using the bond pricing formula with the new yield) Is it higher/lower than the approximation from (b)? d. Recalculate (b) and (c) for an increase of 0.3%. Is the actual new price higher/lower than the duration approximation value? e. The duration approximation will always underestimate the new bond price (for both increases and decreases in rates). Can you try to explain why that is?