1 A life insurance company issues a with-profit endowment assurance policy with a sum assured of 250,000+100y to a life aged 16+x exact. The policy will mature at age 65 exact. Premiums of paid annually in advance throughout the term of the policy and death benefits are paid at the end of year of death. Simple reversionary bonuses of 2.25% per annum of the basic sum assured vest at the start of the policy year (i.e. the death benefit does include any bonus relating to the policy year of death). x=24, y=300, z=30 Basis: Mortality AM92 Select Interest rate 4% per annum Initial Expenses 280 + 40% annual premium Renewal Expenses 50 reducing by 1.8868% compound at the start of each policy year from year 2. The first reduction will be at the start of year 3 (so the renewal expenses are assumed to be 50 at the start of year 2 and 50 x (1 0.018868) at the start of year 3 and so on). a) Calculate the gross premium on the above basis. [9] b) Calculate the gross premium retrospective reserve at the end of the second policy year on the above basis and assuming that bonus additions have followed the assumptions above. [8] Consider the gross prospective reserve at the end of the second policy year on the above basis except that an interest rate of 3% per annum is used. c) Without performing any further calculations, explain how this reserve would compare with your answer to b). [3] [Total 20] 1 A life insurance company issues a with-profit endowment assurance policy with a sum assured of 250,000+100y to a life aged 16+x exact. The policy will mature at age 65 exact. Premiums of paid annually in advance throughout the term of the policy and death benefits are paid at the end of year of death. Simple reversionary bonuses of 2.25% per annum of the basic sum assured vest at the start of the policy year (i.e. the death benefit does include any bonus relating to the policy year of death). x=24, y=300, z=30 Basis: Mortality AM92 Select Interest rate 4% per annum Initial Expenses 280 + 40% annual premium Renewal Expenses 50 reducing by 1.8868% compound at the start of each policy year from year 2. The first reduction will be at the start of year 3 (so the renewal expenses are assumed to be 50 at the start of year 2 and 50 x (1 0.018868) at the start of year 3 and so on). a) Calculate the gross premium on the above basis. [9] b) Calculate the gross premium retrospective reserve at the end of the second policy year on the above basis and assuming that bonus additions have followed the assumptions above. [8] Consider the gross prospective reserve at the end of the second policy year on the above basis except that an interest rate of 3% per annum is used. c) Without performing any further calculations, explain how this reserve would compare with your answer to b). [3] [Total 20]