6. For a 3-year term insurance on (65), you are given: (1) The death benefit is $250,000. (ii) The death benefit is payable at the moment of death. (iii) The annual gross premium is G payable annually in advance. (iv) Expenses prior to issue are $500 and 40% of premium and are paid at time 0. (v) Expenses for years after the first are $20 and 3% of premium payable immediately after the receipt of each gross premium. (vi) Settlement expenses are $ 700 paid at the moment of death. (vii) The model includes lapses, but there are no cash values payable on lapse. (viii) There are reserves at time 1 and 2. (ix) The annual effective rate of interest is 7.50% in all periods. The cash flow/profit table as a function of the premium G is as given below (with interest values missing). This profit table is per starting individual (i.e. the profit signature). time Premium EOY Expenses Interest Increase in Reserves 0 Death Benefits BOY Expenses Paid -$500-0.4G -$2,592.62 $0.00 $5,056.39 $19.50-0.029256G -$6,689.60-$17.20-0.025803G 1 2 3 G 0.9752G 0.8601G $0.00 -$7.26 -$14.16 -$18.73 $0.00 -$243.79 $63.17 $180.62 a) Calculate the reserves at times 1 and 2 per starting individual. (10 Marks) b) Fill in the interest column as a function of the premium G. (10 Marks) c) Calculate the profit signature as a function of the premium G for times 0 to 3 inclusive. (10 Marks) d) Calculate the premium that needs to be charged at a 15% annual effective hurdle rate. (10 Marks) e) Now assume the policy is a participating policy, with 60% of profits in years 2 and 3 returned to policyholders (if positive). If the premium in part d) were charged, what would be the expected present value of the profit returned to shareholders at 15% (10 Marks) f) Calculate the premium that should be charged on the participating policy described in part 3 at a 15% annual effective hurdle rate. (10 Marks) 6. For a 3-year term insurance on (65), you are given: (1) The death benefit is $250,000. (ii) The death benefit is payable at the moment of death. (iii) The annual gross premium is G payable annually in advance. (iv) Expenses prior to issue are $500 and 40% of premium and are paid at time 0. (v) Expenses for years after the first are $20 and 3% of premium payable immediately after the receipt of each gross premium. (vi) Settlement expenses are $ 700 paid at the moment of death. (vii) The model includes lapses, but there are no cash values payable on lapse. (viii) There are reserves at time 1 and 2. (ix) The annual effective rate of interest is 7.50% in all periods. The cash flow/profit table as a function of the premium G is as given below (with interest values missing). This profit table is per starting individual (i.e. the profit signature). time Premium EOY Expenses Interest Increase in Reserves 0 Death Benefits BOY Expenses Paid -$500-0.4G -$2,592.62 $0.00 $5,056.39 $19.50-0.029256G -$6,689.60-$17.20-0.025803G 1 2 3 G 0.9752G 0.8601G $0.00 -$7.26 -$14.16 -$18.73 $0.00 -$243.79 $63.17 $180.62 a) Calculate the reserves at times 1 and 2 per starting individual. (10 Marks) b) Fill in the interest column as a function of the premium G. (10 Marks) c) Calculate the profit signature as a function of the premium G for times 0 to 3 inclusive. (10 Marks) d) Calculate the premium that needs to be charged at a 15% annual effective hurdle rate. (10 Marks) e) Now assume the policy is a participating policy, with 60% of profits in years 2 and 3 returned to policyholders (if positive). If the premium in part d) were charged, what would be the expected present value of the profit returned to shareholders at 15% (10 Marks) f) Calculate the premium that should be charged on the participating policy described in part 3 at a 15% annual effective hurdle rate. (10 Marks)