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# ct52005-2010 - Faculty of Actuaries Institute of Actuaries...

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CT5 A2005 2 1 Explain the difference between a profit vector and a profit signature. [2] 2 A 20-year temporary annuity-due of 1 per annum is issued to a life aged 50 exact. (a) Express the expected present value of the annuity in terms of an assurance function. (b) Hence calculate the value using the mortality table AM92 Ultimate with 4% interest. [3] 3 A life insurance company sells an annual premium whole life assurance policy where the sum assured is payable at the end of the year of death. Expenses are incurred at the start of each policy year, an d claim expenses are nil. (a) Write down a recursive relationship between the gross premium provisions at successive durations, with provisions calculated on the premium basis. Define all the symbols that you use. (b) Explain in words the meaning of the relationship. [4] 4 A life insurance company issues an annuity to a life aged 60 exact. The purchase price is £200,000. The annuity is payable monthly in advance and is guaranteed to be paid for a period of 10 years and for the whole of life thereafter. Calculate the annual annuity payment. Basis: Mortality AM92 Ultimate Interest 6% per annum [4]
CT5 A2005 3 PLEASE TURN OVER 5 A three-state transition model is shown in the following diagram: Assume that the transition probabilities are constant at al l ages with = 2%, = 4%, = 1% and = 5%. Calculate the present value of a sickness benefit of £2,000 p.a. paid continuously to a life now aged 40 exact and sick, during this period of sickness, discounted at 4% p.a. and payable to a maximum age of 60 exact. [4] 6 Calculate the probability of survival to age 60 exact using ELT15 (Males) for a life aged 45½ exact using two approximate methods. State any assumptions you make. [5] 7 A joint life annuity of 1 per annum is payable continuously to lives currently aged x and y while both lives are alive. The present value of the annuity payments is expressed as a random variable, in terms of the joint future lifetime of x and y .

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ct52005-2010 - Faculty of Actuaries Institute of Actuaries...

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