B9. Suppose you have just taken over as head of risk management at Australian Life Insurance Services, Inc. (ALIS). Except for one annuity that makes quarterly $10,000 payments to retirees, the risk appears to be adequately hedged. This quarterly-paying annuity makes its last $10,000 payment on 31 December 2022. Payments are made quarterly on 31 March, 30 June, 30 September, and 31 December. For simplicity, assume that payments are made on these dates, even if they are a holiday or weekend. Today is 3 November 2021 and there are 58 days to the next annuity payment. Consider this annuity risk free (it is risk-free from the perspective of the insurance company). Assume that the term structure is flat, and that the bond equivalent yield for risk-free debt that pays coupons quarterly is 4% per annum. B9a. What is the present value of this annuity? [5 marks] B9b. What maturity zero coupon government bond would perfectly immunise this annuity obligation today (3 November 2021)? [5 marks] B9. Suppose you have just taken over as head of risk management at Australian Life Insurance Services, Inc. (ALIS). Except for one annuity that makes quarterly $10,000 payments to retirees, the risk appears to be adequately hedged. This quarterly-paying annuity makes its last $10,000 payment on 31 December 2022. Payments are made quarterly on 31 March, 30 June, 30 September, and 31 December. For simplicity, assume that payments are made on these dates, even if they are a holiday or weekend. Today is 3 November 2021 and there are 58 days to the next annuity payment. Consider this annuity risk free (it is risk-free from the perspective of the insurance company). Assume that the term structure is flat, and that the bond equivalent yield for risk-free debt that pays coupons quarterly is 4% per annum. B9a. What is the present value of this annuity? [5 marks] B9b. What maturity zero coupon government bond would perfectly immunise this annuity obligation today (3 November 2021)? [5 marks]