Refer to the attachment for the questions.

5 A life insurance company issues a number of 3-year term assurance contracts to lives aged style exactly 60. The sum assured under each contract is f200,000, payable immediately on death. Premiums are payable annually in advance for the term of the policy, ceasing on earlier death. The company carries out profit tests for these contracts using the following assumptions: Initial expenses: E200 plus 35% of the first year's premium Renewal expenses: E25 plus 3% of the annual premium, incurred at the beginning of the second and subsequent years Mortality: AM92 Ultimate Investment return: 7% per annum Risk discount rate: 15% per annum Reserves: One year's office premium (i) Show that the office premium, to the nearest pound, is E2,610, if the net present value of the profit is 25% of the office premium. [10] Calculate the expected in-force cashflows if the company holds zero reserves throughout the contract, using a premium of exactly f2,610. [2] (ili) Explain why the company might not hold reserves for this contract and the impact on profit if it did not hold any reserves. [3] [Total 15] 6 A 5-year unit-linked endowment assurance is issued to a male aged exactly 55. The expected yle year-end cashflows in the non-unit fund, (NUCF), (t = 1, .. , 5) per policy in force at the start of Year t are: Year t 1 2 3 4 5 (NUCF) -200 +20 +45 -60 +480 You are given: Independent probabilities of mortality: AM92 Select Independent probabilities of withdrawal: 0.1 for Years 1 and 2 0.05 for Years 3 and 4 0 for Year 5 Withdrawals can occur at any time over the policy year. Calculate the net present value of profit at a risk discount rate of 10% pa assuming that the company holds no non-unit reserves. [4]The rate of interest earned on non-unit reserves is assumed to be 8% pa. (ii) (a) Calculate the reserves that are required at times t = 1, .., 4 in order to zeroise future negative cashflows. (b) Calculate the net present value of the policy assuming that the company holds the non-unit reserves calculated in (i)(a). [6] (iii) Without carrying out any more calculations, explain the effect on the net present value if non-unit reserves earned interest at the rate of 10% pa. [2] [Total 12] 7 A special endowment policy pays a sum assured of $20,000 to a life who is currently aged exactly yle 57 after three years or at the end of the year of earlier death. Annual reversionary bonuses are declared at the end of each policy year, and an additional terminal bonus is payable at maturity only. Policies may be surrendered only at the end of each policy year. On surrender, the policyholder receives a return of premiums with interest calculated at the rate of 3% per annum. A level premium of $8,000 is paid at the start of each year. The premium basis is as follows: Interest: 7% per annum Mortality: AM92 Select Surrender rates: 15% of all policies in force at the end of year 1 5% of all policies in force at the end of year 2 Reversionary bonuses: 6% per annum compound Terminal bonus: 10% of all other benefits payable at maturity Expenses: Initial E500 Renewal E30 at start of year 2 E35 at start of year 3 Termination E100 per termination (death, surrender or maturity) Reserves: Net premium reserves, using AM92 Ultimate mortality and 4% per annum interest (i) Calculate the profit signature for this policy according to the premium basis. [14] (ii) By accumulating the elements of the profit signature to the maturity date, explain briefly whether you think the company expects to declare the bonus rates it has assumed in its premium basis, assuming all the other assumptions in the basis are realistic. [2] [Total 16]