(10) Please write your answer in the answer book provided. Show your workings. Circle your final answer. (a) A life insurer sells a 15-year term certain annuity which pays an annual effective rate of interest i = 4% to the policyholder. If the customer wants to purchase the annuity which pays $1,500 at the end of each year for 15 years, what is the single premium he/she needs to pay the Insurer? [1 mark] (b) The same life insurer sells a 15-year term certain annuity which pays an annual effective rate of interest i = 4% to the policyholder. If the customer wants to purchase the annuity which pays $1,500 at the end of each month for 10 years, what is the single premium he/she needs to pay the Insurer? [1 mark] (11) Please write your answer in the answer book provided. Show your workings. Circle your final answer. (a) John contributes $X at the start of each year for 40 years into his superannuation fund. Assuming the superannuation fund earns 3% per interest rate effective for 40 years, if John's target lump sum at the end of 40 years is $1,500,000, then what should X be? [1 mark] (b) Mary contributes $Y at the start of each month for 40 years into her superannuation fund. Assume the superannuation fund earns 3% per interest rate effective, if Mary's target lump sum at the end of 40 years is $1,500,000, then what should Y be? [1 mark]