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A life insurance company sells 1,000 whole life annuities on 1 January 2007 to policyholders aged 65 exact. Each annuity is for $25,000 payable annually in arrear. 5 annuitants die during 2007. The office holds reserves using the following basis: Mortality PFA92C20 Interest 4% per annum Calculate the profit or loss from mortality for this group for the year ending 31 December 2007. (4] (ii) Explain why the mortality profit or loss has arisen. 121 [Total 6] A new member aged 35 exact, expecting to earn $40,000 in the next 12 months, has just joined a pension scheme. The scheme provides a pension on retirement for any reason of 1/60th of final pensionable salary for cach year of service, with fractions counting proportionately. Final pensionable salary is defined as the average salary over the three years prior to retirement. Members contribute a percentage of salary, the rate depending on age. Those under age 50 contribute 4% and those age 50 exact and over contribute 5%. The employer contributes a constant multiple of members' contributions to meet exactly the expected cost of pension benefits. Calculate the multiple needed to meet this new member's benefits. All elements of the valuation basis are contained in the Example Pension Scheme Table in the Formulae and Tables for Examinations. [6] Calculate the variance of the present value of benefits under an annuity payable to a life aged 35 exact. The annuity has payments of ] per annum payable continuously for life. Basis: Mortality L = 0.02 throughout Interest 8 =0.05 [7] A life insurance company has reviewed its mortality experience. For each age, it has pooled all the deaths and corresponding exposures from its entire portfolio over the previous ten years, and derived a single mortality table. List three types of selection which might be likely to produce heterogencity in this particular investigation. In each case, explain the nature of the heterogeneity and how it could be caused, and state how the heterogeneity could be reduced. [9]A life insurance company sells 1,000 whole life annuities on 1 January 2007 to policyholders aged 65 exact. Each annuity is for $25,000 payable annually in arrear. 5 annuitants die during 2007. The office holds reserves using the following basis: Mortality PFA92C20 Interest 4% per annum Calculate the profit or loss from mortality for this group for the year ending 31 December 2007. (4] (ii) Explain why the mortality profit or loss has arisen. 121 [Total 6] A new member aged 35 exact, expecting to earn $40,000 in the next 12 months, has just joined a pension scheme. The scheme provides a pension on retirement for any reason of 1/60th of final pensionable salary for cach year of service, with fractions counting proportionately. Final pensionable salary is defined as the average salary over the three years prior to retirement. Members contribute a percentage of salary, the rate depending on age. Those under age 50 contribute 4% and those age 50 exact and over contribute 5%. The employer contributes a constant multiple of members' contributions to meet exactly the expected cost of pension benefits. Calculate the multiple needed to meet this new member's benefits. All elements of the valuation basis are contained in the Example Pension Scheme Table in the Formulae and Tables for Examinations. [6] Calculate the variance of the present value of benefits under an annuity payable to a life aged 35 exact. The annuity has payments of ] per annum payable continuously for life. Basis: Mortality L = 0.02 throughout Interest 8 =0.05 [7] A life insurance company has reviewed its mortality experience. For each age, it has pooled all the deaths and corresponding exposures from its entire portfolio over the previous ten years, and derived a single mortality table. List three types of selection which might be likely to produce heterogencity in this particular investigation. In each case, explain the nature of the heterogeneity and how it could be caused, and state how the heterogeneity could be reduced. [9]
