Exercise 12.12 A life aged 60 purchases a deferred life annuity, with a five- year deferred period. At age 65 the annuity vests, with payments of $20 000 per year at each year end, so that the first payment is on the 66th birthday. All payments are contingent on survival. The policy is purchased with a single premium. If the policyholder dies before the first annuity payment, the insurer returns her gross premium, with interest of 5% per year, at the end of the year of her death. (a) Calculate the single premium using the following premium basis: 0.9(0.00022 +2.7 10-6 x 1.124*) for all x 6% per year before vesting; 5% per year thereafter $275 at issue plus $20 with each annuity payment. Survival model: Hx Interest: Expenses: (b) Gross premium reserves are calculated using the premium basis. Calculate the year end rescrves (after the annuity payment) for each year of the contract. Exercise 12.12 A life aged 60 purchases a deferred life annuity, with a five- year deferred period. At age 65 the annuity vests, with payments of $20 000 per year at each year end, so that the first payment is on the 66th birthday. All payments are contingent on survival. The policy is purchased with a single premium. If the policyholder dies before the first annuity payment, the insurer returns her gross premium, with interest of 5% per year, at the end of the year of her death. (a) Calculate the single premium using the following premium basis: 0.9(0.00022 +2.7 10-6 x 1.124*) for all x 6% per year before vesting; 5% per year thereafter $275 at issue plus $20 with each annuity payment. Survival model: Hx Interest: Expenses: (b) Gross premium reserves are calculated using the premium basis. Calculate the year end rescrves (after the annuity payment) for each year of the contract