Suppose a 3-year Government Bond with a par value of $1 million and a coupon rate of 2% per annum payable semi-annually is currently trading at a yield to maturity of 1% per annum convertible half- yearly. a. Calculate the modified (i.e. effective) duration for this bond and express your answer in years. (7 marks) b. The convexity of a 2.5-year annuity with annual payments of $20,000 payable semi-annually and generating an effective semi-annual yield of 0.5% is 4. Make use of this information to calculate the convexity for the bond. (3 marks) C. Estimate the price change (in percentage) of the bond for a 1% rise in the annual yield to maturity convertible half-yearly using the two-term Taylor series expansion. Then compare this estimate with the actual percentage change in price. (3 marks) Suppose a 3-year Government Bond with a par value of $1 million and a coupon rate of 2% per annum payable semi-annually is currently trading at a yield to maturity of 1% per annum convertible half- yearly. a. Calculate the modified (i.e. effective) duration for this bond and express your answer in years. (7 marks) b. The convexity of a 2.5-year annuity with annual payments of $20,000 payable semi-annually and generating an effective semi-annual yield of 0.5% is 4. Make use of this information to calculate the convexity for the bond. (3 marks) C. Estimate the price change (in percentage) of the bond for a 1% rise in the annual yield to maturity convertible half-yearly using the two-term Taylor series expansion. Then compare this estimate with the actual percentage change in price