3. Duration (30 points): Consider the bond in Question 1 (7 year maturity bond that makes semiannual coupon payments, has a coupon rate of 1.75%, a face value of 1000, and a yield to maturity of 1.46%). Calculate the duration (Macaulay duration) for the bond. Hint: The easiest way to do this will be to adapt the spreadsheet in the file PS4.xls. a. b. Describe intuitively what the bond's Macaulay duration measures. If the bond was a zero coupon bond, what would have been its Macaulay duration? c. Calculate the modified duration of the bond. d. If the market yield increases by 20 basis points (0.2 percent), what is the percentage change in the bond's price as predicted using the bond's duration calculated in b.? e. Now calculate the bond price before and after the change in yield directly (hint: you can use the PS Excel spreadsheet in PS4.xls to do this.) How good is the approximation of the bond's price change you used in c.? f. Is the predicted price higher or lower than the actual price? Is this what you expected