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10 A male and a female, aged 60 and 64 respectively, take out a policy under which the benefits are: A lump sum of f50,000 payable at the end of the year of the first death provided this occurs within 10 years. An annuity payable annually in advance with the first payment due to be made 10 years from the date of issue. The annuity payments will be f10,000 po for as long as both lives are still alive or $5,000 while only one of them is alive. Level premiums are payable annually in advance for at most 10 years and will cease on the first death if this occurs earlier. Calculate the amount of the annual premium on the following basis: Interest: 4% pa Mortality: PMA92C20 for the male life and PFA92C20 for the female life Expenses: Initial: E750 Renewal: 3% of each premium excluding the first [8] 11 A pension scheme provides the following benefit to the spouse of a member, following the death yle of the member in retirement: A pension of f25,000 po payable during the lifetime of the spouse, but ceasing 20 years after the death of the member if that is earlier. All payments are made on the anniversary of the member's retirement. Calculate the expected present value of the spouse's benefit in the case of a female member retiring now on her 65th birthday, who has a husband aged exactly 55. Basis: Mortality: PMA92C20 for the male life, PFA92C20 for the female life Interest: 4% pa effective8 An insurance company is considering the sale of a 'critical illness extra' term assurance policy. He The critical illness benefit is 25,000, payable immediately on diagnosis of a critical illness within the 25-year term. The death benefit is $75,000, payable immediately on death during the term. Only one benefit is payable under any one policy and once the benefit has been paid, both the premiums and the cover cease. Annual premiums of EP pa are payable continuously while the policy is in force. The company assesses the profitability of the policy using the following multiple state model: Ox Healthy (H) Critically sick (S) Dead (D) Px is defined as the probability that a life who is in state a at age x (a = H, 5, D) is in state b at age x + t (t > 0 and b = H,S,D). (1) Suggest, with reasons, one group of customers the insurance company may wish to target in their marketing of this policy. [1] (ii) Express in integral form, using the probabilities and the forces of transition, the expected present value of the profit from one such policy with an annual premium of f1,200 that has just been sold to a life aged exactly 50. [2] After careful consideration, the company modifies the policy by changing both the death benefit and the critical illness benefit to be $50,000. (iii) Explain how this modification could considerably reduce the cost of assessing claims. [2] (iv) Given that #* =0.0006 and ox =0.0014 for all 45 S x$70, and that the force of interest is 4% pa, calculate the expected present value of the benefits for the modified policy sold to a life aged exactly 45. [3] [Total 8]