without using a financial calculator or excel. Please provide all formula used and variables with clear steps

(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]