for actuarial science, reserves and policy values

6. Your company issues whole life annuities to a group of lives age 70 . For each policy, you are given: i. The annuity pays $2000 at the end of each year. ii. The single gross premium is $26,600. iii. Profits are based on gross premium reserves. iv. The gross premium reserve at the end of year 10 is $8929.18 per policy. v. Expenses are paid at the end of each year for any policyholder who does not die during the year. During year 11 , anticipated and actual experience are as follows: 1000 such policies are in force at the beginning of year 11. For year 11 a) Provide a revised version of the recursive formula for calculating the policy value of the annuity described above. b) Calculate 11V. c) Calculate the total profit. d) Calculate the profit by source in the order mortality, interest, expenses. 6. Your company issues whole life annuities to a group of lives age 70 . For each policy, you are given: i. The annuity pays $2000 at the end of each year. ii. The single gross premium is $26,600. iii. Profits are based on gross premium reserves. iv. The gross premium reserve at the end of year 10 is $8929.18 per policy. v. Expenses are paid at the end of each year for any policyholder who does not die during the year. During year 11 , anticipated and actual experience are as follows: 1000 such policies are in force at the beginning of year 11. For year 11 a) Provide a revised version of the recursive formula for calculating the policy value of the annuity described above. b) Calculate 11V. c) Calculate the total profit. d) Calculate the profit by source in the order mortality, interest, expenses