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Andrew is now aged 30 exact. He wants to purchase a life annuity product to support his life after retirement. Assume that he will retire at the age of 65. The annuity payment will be made yearly in arrears with a benefit of $10,000 in each year. The benefits will cease upon his death. Use the AM92 ultimate mortality with 4% interest rate p.a. (a) If Andrew decides to purchase the annuity with a single payment now, calculate the amount of this payment. (3 marks) (b) Suppose instead Andrew decides to pay for the annuity with yearly level instalments commencing at age 55 exact. Instalments are paid while Andrew is alive with a maximum of ten instalments paid. Calculate the amount of the level instalment (3 marks) (c) Andrew's brother, Tom, currently aged 35 exact, buys a whole of life insurance with sum insured of $500,000 payable at the end of the year of death. Premiums are payable by Tom monthly in advance, starting immediately and continuing until death. Suppose also the following expenses are incurred by the life office: Acquisition expense: $100+50% of the first year total premium, at issuance. Maintenance expense: $10+ 2% of the total annual premium, at the start of each year. Claim processing expense: 2% of sum insured, at time of claim payment. Calculate the gross annual premium rate. (4 marks) Andrew is now aged 30 exact. He wants to purchase a life annuity product to support his life after retirement. Assume that he will retire at the age of 65. The annuity payment will be made yearly in arrears with a benefit of $10,000 in each year. The benefits will cease upon his death. Use the AM92 ultimate mortality with 4% interest rate p.a. (a) If Andrew decides to purchase the annuity with a single payment now, calculate the amount of this payment. (3 marks) (b) Suppose instead Andrew decides to pay for the annuity with yearly level instalments commencing at age 55 exact. Instalments are paid while Andrew is alive with a maximum of ten instalments paid. Calculate the amount of the level instalment (3 marks) (c) Andrew's brother, Tom, currently aged 35 exact, buys a whole of life insurance with sum insured of $500,000 payable at the end of the year of death. Premiums are payable by Tom monthly in advance, starting immediately and continuing until death. Suppose also the following expenses are incurred by the life office: Acquisition expense: $100+50% of the first year total premium, at issuance. Maintenance expense: $10+ 2% of the total annual premium, at the start of each year. Claim processing expense: 2% of sum insured, at time of claim payment. Calculate the gross annual premium rate. (4 marks)

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