Economics application questions
7.1 Explain briefly how a life office calculates the new sum assured or annual premium on the alteration or conversion of an existing policy. 7.2 A life office issued a whole life without profits policy to a woman aged 30, with sum assured of f110,000. Premiums were payable annually in advance throughout life, and the sum assured was payable at the end of the year of death. Immediately before payment of the 15th premium, the policyholder requests that the policy be converted to a without profits endowment assurance for the same sum assured, payable on maturity at age 60 or at the end of the year of death, if before age 60. The office calculates premiums and maintains reserves on the basis of A 1967-70 ultimate mortality and 4% per annum interest, with expenses of 4% of each premium. Expenses of alteration may be ignored. Find the revised annual premium. 7.3 On 1 January 1972 an office issued a large number of 40-year endowment assurance policies, each with sum assured f1000 (payable at the end of the year of death, if this occurs within the term) to a group of lives all then aged 25. On 31 December 1988 there were 8567 policies still in force. During 1989 there were 13 deaths among the policyholders. Find the actual death strain, the expected death strain and the mortality profit or loss for the business in 1989, using the following basis for all calculations: mortality: A1967-70 select interest: 4% p.a. expenses: none 4 On 1 January 1991, a life office issued a number of identical special endowment assurances to lives then aged 45. Each policy had a term of 15 years and level annual premiums were payable throughout the term. On survival to the end of the term, a sum assured of 25000 is payable. On death before the end of the term, a sum assured of f1000 is payable at the end of the year of death and, in addition, all premiums paid are returned without interest. The premium basis for these policies was as follows: mortality: A1967-70 select interest: 4% p.a. openses: Nil (i) Show that the annual premium for each of these policies is 1242.27. (ii) Calculate the reserve, on the premium basis, on 1 January 1996 for one of these policies, assuming that the premium then due is unpaid. (iii) On 1 January 1995, a total of 10,000 of these policies were still in force. In 1995, 47 of these lives died, ten policies were surrendered, and the life office earned 4% interest on its investments. Expenses were negligible in 1995. The surrenders all took place at the end of 1995, and the office gave surrender values equal to 95% of the reserve on the premium basis. Calculate the profit or loss to the office in 1995 from this block of business in respect of (a) mortality , and(b) surrenders. 7.5 A life office has issued a 5-year decreasing temporary assurance to a life aged 60. The sum assured, payable at the end of the year of death, is 6100,000 if the life dies in the first year, 690.000 if the life dies in the second year, and so on, decreasing by f10,000 each year. Level annual premiums are payable throughout the term of the policy. The premium and reserve basis for this policy is as follows: mortality: A1967-70 Ultimate interest: 4% p.a. expenses: Nil (i) Calculate the annual premium for the policy. (ii) Write down a relationship between the reserve at integer duration t and the reserve at duration t + 1
