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Exercise 7.16 An insurer issues identical deferred annuity policies to 100 independent lives aged 60 at issue. The deferred period is 10 years, after which the annuity of $10000 per year is paid annually in advance. Level premiums are payable annually throughout the deferred period. The death benefit during deferment is $50000, payable at the end of the year of death. The basis for premiums and policy values is: Survival model: Standard Ultimate Life Table Interest: 5% per year effective Expenses: None (a) Calculate the premium for each contract. (b) Write down the recursive relationship for the policy values, during and after the deferred period. (c) Calculate the death strain at risk in the second year of the contract, for each contract still in force at the start of the year. (d) Calculate the death strain at risk in the 13th year of the contract, per contract in force at the start of the year. (e) One year after the issue date, 98 policies remain in force. In the second year, two lives die. Calculate the total mortality profit in the second year, assuming all other experience follows the assumptions in the premium basis. (f) Twelve years after the issue date 80 lives survive; in the 13th year there are four deaths. Calculate the total mortality profit in the 13th year. Exercise 7.16 An insurer issues identical deferred annuity policies to 100 independent lives aged 60 at issue. The deferred period is 10 years, after which the annuity of $10000 per year is paid annually in advance. Level premiums are payable annually throughout the deferred period. The death benefit during deferment is $50000, payable at the end of the year of death. The basis for premiums and policy values is: Survival model: Standard Ultimate Life Table Interest: 5% per year effective Expenses: None (a) Calculate the premium for each contract. (b) Write down the recursive relationship for the policy values, during and after the deferred period. (c) Calculate the death strain at risk in the second year of the contract, for each contract still in force at the start of the year. (d) Calculate the death strain at risk in the 13th year of the contract, per contract in force at the start of the year. (e) One year after the issue date, 98 policies remain in force. In the second year, two lives die. Calculate the total mortality profit in the second year, assuming all other experience follows the assumptions in the premium basis. (f) Twelve years after the issue date 80 lives survive; in the 13th year there are four deaths. Calculate the total mortality profit in the 13th year