Solve the following questions properly

Under a 10-year 'double endowment' assurance policy issued to a group of lives aged 50, a sum assured of $10,000 is payable at the end of the year of death and E20,000 is paid if the life survives to the maturity date. Premiums are payable annually in advance. You are given the following information: reserve at the start of the 8th year (per policy in force): f12,951 number of policies in force at the start of the 8th year: 200 number of deaths during the 8th year: 3 annual premium (per policy) (1,591 Assuming that reserves are calculated according to the basis specified below, calculate the profit or loss arising from mortality in the 8th year. [5] (Wi) Comment on your results. [1] Basis: Mortality: ELT15 (Males) Interest: 4% pa effective Expenses: None [Total 6] On 1 January 2012, a life insurance company issued joint life whole life assurance policies. Each policy was issued to a male life aged 65 exact and a female life aged 60 exact. A sum assured of 75,000 is payable immediately on the death of the second of the lives to die. Premiums of 1,395.11 are payable annually in advance for each policy while at least one of the lives is alive. At the beginning of 2014, there were 5,997 policies in force. For all of these policies, both lives were still alive. During 2014, the following experience was observed: for 2 policies, both lives died for 12 policies, only the male life died for 8 policies, only the female life died. Calculate, showing all your workings, the mortality profit or loss for the group of policies for the calendar year 2014. Basis: Mortality: PMA92C20 for the male PFA92C20 for the female Interest: 4% per annum Expenses: Ignore [10]8 An insurance company is considering the sale of a 'critical illness extra' term assurance policy. The critical illness benefit is f25,000, 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 po 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 (S) HX Dead (D) " 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 + t (t > 0 and b = H,5,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 E1,200 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 * $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]9 A life insurance company uses a three-state model as shown below to calculate premiums for a yle two-year combined sickness and endowment assurance policy issued to healthy policyholders aged 58. H = healthy S = sick Px Hx Vx D = dead Premiums are payable at the start of each policy year and are waived if the policyholder is sick at the time the premium is due. At the end of each policy year a benefit of E10,000 is payable if the life is then sick. A sum assured of E15,000 is payable at the end of the year of death if this occurs during the term of the policy, or at the end of the term if the life is alive and has never claimed any sickness benefit. 5, denotes the state occupied by the policyholder at age 58 + t , so that So = H (healthy) and S, = H, S or D (healthy, sick or dead) for t = 1, 2. The transition probabilities used by the insurer are defined in the following way: P58+t = P(5,+1 = k |S, = j) where for t = 0,1: HD P58+t = 0.02 HS P58+t = 0.1 SD .SS P58+t = 0.05 P58+t = 0.09 Calculate the annual premium for this policy using the equivalence principle, based on the above transition probabilities and the following additional assumptions: Interest: 3% pa effective Initial expenses: f200 incurred at outset Renewal expenses: f40 at time 1, whether the policyholder is healthy or sick Claim expense: f30 at the date of payment of any benefit [8]