1.
(a) A life aged 45 exact takes out a temporary level annuity-due which provides level payments of £10,000 per annum payable at the end of each year for 10 years or until death, whichever is earlier. Calculate the expected present value and the standard deviation of the present value of this policy. Basis: 4% per annum interest, AM92 mortality. [9 marks]
(b) Assuming the AM92 Ultimate table applies, calculate 1.75q40 using the assumptions of
(i) uniform distribution of death and
(ii) constant force of mortality. [10 marks]
(c) A male life aged 40 exact takes out a special assurance policy with a term of 15 years. Under the policy, if he dies before age 55 exact, his beneficiaries will receive the benefits of £20,000 per annum, payable at the end of each year until the end of the term, with the first payment being made at the end of year of his death. Assuming AM92 ultimate table and the interest rate of 4%, calculate the expected present value of the policy. [6 marks]
Total: 25 marks
2.
(a) A life office issues a 10-year with-profits endowment assurance policy to a life aged 40 exact. The initial sum assured of £5,000 plus declared reversionary bonuses are payable on survival to the end of the term or at the end of the year of death if earlier. The premiums are payable annually in advance throughout the term or until death if earlier. Calculate the annual gross premium payable by the policyholder.
Basis: Reversionary bonuses A simple rate of 5% per annum of the initial sum assured, from the second year onwards Interest 4% per annum Mortality AM92 Select Initial expenses £100 Renewal expenses 2% of the annual gross premiums payable at the start of the second and subsequent policy years Claim expense £100 [15 marks]
(b) A married couple, husband aged 50 exact and wife aged 55 exact, took out a joint life assurance policy which pays the sum assured of £20,000 immediately upon the first death of the couple.
(i) Calculate the expected present value of the policy. [5 marks]
(ii) Five years after the couple took out the policy the wife dies at the age of 60 exact and the husband receives the sum assured. He wants to use the money as a one-off premium to buy a reversionary annuity which will pay benefits monthly to his elderly mother, now aged 75 exact, after his death. If his mother dies before he does, no benefit will be paid. Calculate the monthly benefit of the reversionary annuity. [5 marks]
Basis: PMA92C20 for the male, PFA92C20 for the females, 4% per annum interest.
Total: 25 marks
3.
(a) A life office issued a 25-year term assurance policy with a sum assured of £75,000 payable at the end of year of death. Premiums are payable annually in advance for 20 years or until earlier death. On 1 January 2001, the company sold 750 policies to lives then aged 30 exact. By 1 January 2020, 12 policyholders had died. During the year of 2020, a further two policyholders died.
(i) Calculate the net premium reserve per policy at the start and at the end of the year of 2020 using the basis given below. [10 marks]
(ii) Calculate the mortality profit or loss to the life office during the year of 2020. Comment on your results. [5 marks]
Basis: Interest 4% per annum Mortality AM92 Ultimate Expenses Nil
(b) The decrement table extract below is based on the historical experience of a very large multinational company’s workforce.
Recent changes in working conditions have resulted in an estimate that the annual independent rate of withdrawal is now 75% of that previously used. Calculate a revised table assuming no changes to the independent death rates (stating your results to one decimal place). [10 marks] Total: 25 marks
4.
(a) A five-year unit-linked policy issued to a life aged 50 exact has the following pattern of end of year cashflows per policy in force at the start of each year: (−95.21,−30.18,−20.15,77.15,120.29) Calculate the revised profit vector if non-unit reserves are set up to zeroise the negative cashflows, assuming AM92 Ultimate mortality and that reserves earn interest at the rate of 5% per annum. [5 marks]
(b) A life insurance company issues a 2-year unit-linked endowment assurance contract to a male life aged exactly 63, under which level annual premiums of £6,000 are payable in advance throughout the term of the policy, or until earlier death. 102% of each year’s premium is invested in units at the offer price. There is a bidoffer spread in unit values, with the bid price being 95% of the offer price. The annual management charges are 5% of the bid value of the units, deducted at the end of each year before death, surrender or maturity benefits are paid. On the death of the policyholder during the term of the policy, there is a benefit payable at the end of the year of death of £10,000, or the full bid value of the units allocated to the policy, if greater. On maturity, the full bid value of the units is payable. The policyholder may surrender the policy only at the end of the first policy year. The surrender value is equal to 87% of the bid value of the units.
Calculate the profit vector on this contract, assuming that the company does not hold non-unit reserves. [20 marks]
Total: 25 marks
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