a. Mary invests a 5% annual coupon bond with three years to maturity. The bond has a yield-to-maturity of 9%. The par value is $1,000. i. Calculate the modified duration of the bond. (5 marks) ii. If the yield increases by 50 basis points, what is the new bond price using the duration? ( 3 marks) b. John needs to pay $55,000,$60,000 and $65,000 at the end of next 3 years respectively. The market interest rate is 4% per annum. i. What will be the duration of John's payment obligation? ( 4 marks) ii. Suppose John plans to fully fund the obligation using both 6-month zero coupon bonds and perpetuities. Determine how much (in market value) of each of these bonds John will hold in the portfolio