Microeconomics 001

A life insurance company issues 20-year temporary assurance policies to lives aged 45. The sum assured, which is payable immediately on death, is $400,000 for the first 10 years, and $100,000 thereafter. Level annual premiums are payable in advance for 20 years, or until earlier death. The premium basis is: Mortality: AM92 Ultimate Interest: 4% per annum Expenses: nil. (i) Show that the premium payable is approximately $870.25 per annum. [4] (ii) Find the net premium reserve ten years after the commencement of the policy, immediately before the payment of the eleventh premium, assuming the reserving basis is the same as the premium basis. [4] (iii) Give an explanation of your numerical answer to part (ii). Describe the disadvantages to the insurance company of issuing this policy. [3] (iv) How could the terms of the policy be altered, so as to remove the disadvantages described in part (iii)? [2] [Total 13]A life insurance company sells whole-life assurance policies with a sum assured of (20,000, payable at the end of the year of death. The premium is $420 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: bAs + 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]