25.8!!

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 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 P pa are payable continuously while the policy is in force. The company assesses the profitability of the policy using the following multiple state model: , Healthy (H) Critically sick (5) 4x Dead (D) to 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 agext (t20 and b = H,S,D). Suggest, with reasons, one group of customers the insurance company may wish to target in their marketing of this policy. (1) 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 1,200 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. (1) (iv) Explain how this modification could considerably reduce the cost of assessing claims. [2] Given that Hy = 0.0006 and oy = 0.0014 for all 45 S* 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)