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A special temporary annuity pays $2,000 annually in advance to a man aged exactly 60. The annuity will be paid for two years or until the policyholder's earlier death. If the policyholder survives to his 62nd birthday, he will receive an additional lump sum payment of $5,000. Calculate the expected present value and the standard deviation of the present value of the benefits payable to the policyholder under this contract. Basis: AM92 Ultimate mortality and 4% pa interest. [6]A life insurance company uses the three-state illness-death model as shown below to calculate premiums for a 2-year sickness policy issued to healthy policyholders aged 58. H = healthy S = sick Px Hx D = dead S, denotes the state occupied by the policyholder at age 58+7, so that So = H (healthy) and S, = H, S or D (healthy, sick or dead) for f = 1, 2. The transition intensities used by the insurer are defined in the following way: PS8+1 = P(5, = kIS, = j). 1 =0,1 For / = 0, 1, it is assumed that: HH HS P58+ = 0.92 P58+ = 0.05 SH P38+ = 0.65 SS P38+1 = 0.25 The policy provides a benefit of $5,000 at the end of each year if the policyholder is then sick, and a benefit of $20,000 at the end of the year of death. Calculate the expected present value of the benefits under this policy, assuming an interest rate ofOn 30 June 1999 an annual premium 25-year endowment assurance policy was issued to a life aged 45 who was assumed to be subject to AM92 Select mortality rated down 5 years. Write down an expression in terms of annuities (in which all functions are based on AM92 mortality with no age adjustment) giving the net premium reserve per unit sum assured on 1 July 2004 for this policy, assuming that all premiums due by that date have been paid. [3]