Answer all the questions below

A life insurance company sells whole-life assurance policies with a sum assured of E20,000, payable at the end of the year of death. The premium is f420 payable annually in advance until the death of the policyholder. A life now aged 50 purchased a policy exactly one year ago, and is now due to pay the second annual premium. (i) Find the expected present value of the future loss to the company arising from this policy. [2] (ii) Show that the variance of the present value of the future loss from this policy can be expressed as: b. Aso + c Determine the numerical values of b and c, and the rate of interest used to evaluate Aso . [3] Basis: mortality AM92 Ultimate, interest 4% pa. Ignore expenses. [Total 5](i) Given an investment of (1,000 find the accumulation after 5 years using: (a) simple discount of 8% pa (b) compound discount of 8% pa (c) compound interest of 8% pa. (ii) Given a payment of (2,000 due in 4 years' time, calculate the present value using: (a) simple interest of 3% pa (b) simple discount of 3% pa (c) compound interest of 3% pa