a. A 6% coupon bond paying interest annually has a modified duration of 7 years, sells for $820, and is priced at a yield to maturity of 9%. If the YTM decreases to 8%, what is the predicted change in price ($) using the duration concept? (2 marks) b. A bond with annual coupon payments has a coupon rate of 6%, yield to maturity of 7 % , and Macaulay duration of 12 years. What is the bond's modified duration? (2 marks) c. Which bond has the longest duration? Explain. (3 marks) i. 10-year maturity, 4% coupon. ii. 10-ycar maturity, 9% coupon. ii. 15-year maturity, 4% coupon. iv. 15-ycar maturity, 9% coupon