Question 2 (17 marks) a. Peter buys a 5% annual coupon bond with 4 years to maturity. The bond has a yield-to-maturity of 6%. The par value is $1,000. i. Calculate the duration and modified duration of the bond. (5 marks) ii. If the yield increases to 7.5%, what is the new bond price using the duration concept? (3 marks) b. At the end of next 3 years, you need to pay $50,000,$100,000 and $150,000 respectively. i. If the market interest rate is 5% per annum., what will be the duration of your payment obligation? (4 marks) ii. Suppose you plan to fully fund the obligation using both 6-month zero coupon bonds and perpetuities. Determine how much of each of these bonds (in market value) you will hold in the portfolio