Part 1;
A life insurance company issues a special term assurance policy to two lives aged exactly 50 at the issue date, in return for the payment of a single premium. The following benefits are payable under the contract: (i) In the event of either of the lives dying within 10 years, a sum assured of $100,000 is payable immediately on this death. (ii) In the event of the second death within 10 years, a further sum assured of $200,000 is payable immediately on the second death. Calculate the single premium. Basis: Mortality: A1967-70 Ultimate Interest: 4% per annum Expenses: None [8](i) State the conditions necessary for gross premium retrospective and prospective reserves to be equal. [3] (ii) Demonstrate the equality of gross premium retrospective and prospective reserves for a whole life policy, given the conditions necessary for equality.A life insurance company sells term assurance policies with terms of either 10 or 20 years. As an actuary in the life office, you have been asked to carry out the first review of the mortality experience of these policies. The following table shows the statistical summary of the mortality investigation. In all cases, the central rates of mortality are expressed as rates per 1,000 lives. All policies 10-year policies 20-year policies Age Number Central Number Central Number Central in force mortality in force mortality in force mortality rate rate rate -24 6,991 1.08 6,013 0.86 978 2.12 25-44 6,462 2.05 5,438 1.74 1,024 3.68 45-64 5.815 13.26 4.942 11.55 873 22.94 65- 3,051 75.70 2,570 71.53 481 97.70 Total 22,319 18.963 3.356 (i) Calculate the directly standardised mortality rate and the standardised mortality ratio separately in respect of the 10-year and 20-year policies. In each case, use the "all policies" population as the standard population. [6] (ii) You have been asked to recommend which of these two summary mortality measures should be monitored on a regular basis. Give your recommendation, explaining the reasons for your choice. [3]A life insurance company offers an option on its 10-year without profit term assurance policies to effect a whole life without profits policy, at the expiry of the 10-year term, for the then existing sum assured, without evidence of health. Premiums under the whole life policy are payable annually in advance for the whole of life, or until earlier death. (i) Describe the conventional method of pricing the mortality option, stating clearly the data and assumptions required. Formulae are not required. [3] (ii) A policyholder aged exactly 30 wishes to effect a 10-year without profits term assurance policy, for a sum assured of $100,000. Calculate the additional single premium, payable at the outset, for the option, using the conventional method The following basis is used to calculate the basic premiums for the term assurance policies. Basis: Mortality: A1967-70 Select Interest: 6% per annum Expenses: none [4] (iii) Describe how you would calculate the option single premium for the policy described in part (ii) above using the North American method, stating clearly what additional data you would require and what assumptions you would make. [4] (iv) State, with reasons, whether it would be preferable to use the conventional method or the North American method for pricing the mortality option under the policy described in part (ii) above. [3]
