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An insurance company is considering the sale of a "critical illness extra" term assurance policy. 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. 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 f P pa are payable continuously. The company assesses the profitability of the policy using the following multiple state model: Healthy (H) critically Sick (S) Dead (D) Pr. is defined as the probability that a life who is in state a at age x (a = H, S, D) is in state b at age x + 1 (1 2 0 and b = H, S, D). (i) 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 various forces of transition, the expected present value of one such policy with an annual premium of El,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 the modification could considerably reduce the cost of assessing claims. [2] (iv) You are given My =0.0006, U, =0.03x, Or =0.0014 for all 45