Question 5[3+5+1+4+5=18 marks ] Luxio is an insurer. It has two liabilities of $100 million and \$200 million which are due in 10-year and 20-year's time, respectively. Luxio's assets consist of two zero-coupon bonds and one annuity. These two zero-coupon bonds will pay $22.05 million and $122.004 million respectively, both in 15 -year's time. The annuity pays $X million per annum in arrears for the next t years. Assume the first two conditions of immunisation to small changes in the rate of interest are satisfied for Luxio. The interest rate is 3% per annum effective (and it applies to all assets and liabilities). a) Calculate Macaulay's duration of the liabilities. b) Show that the annuity has t=41. (Hint; you may use the actuarial table.) c) Calculate X. d) Discuss whether Luxio meets the third condition of immunisation. c) Luxio wants to sell the two zero-coupon bonds it has and invest the revenue from selling the bonds in another zero-coupon bond that has a shorter maturity length. Discuss the risks that arise from this. Question 5[3+5+1+4+5=18 marks ] Luxio is an insurer. It has two liabilities of $100 million and \$200 million which are due in 10-year and 20-year's time, respectively. Luxio's assets consist of two zero-coupon bonds and one annuity. These two zero-coupon bonds will pay $22.05 million and $122.004 million respectively, both in 15 -year's time. The annuity pays $X million per annum in arrears for the next t years. Assume the first two conditions of immunisation to small changes in the rate of interest are satisfied for Luxio. The interest rate is 3% per annum effective (and it applies to all assets and liabilities). a) Calculate Macaulay's duration of the liabilities. b) Show that the annuity has t=41. (Hint; you may use the actuarial table.) c) Calculate X. d) Discuss whether Luxio meets the third condition of immunisation. c) Luxio wants to sell the two zero-coupon bonds it has and invest the revenue from selling the bonds in another zero-coupon bond that has a shorter maturity length. Discuss the risks that arise from this