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Question 5.13 A life office is planning to issue a new series of 3-year unit linked endowment policies. Two designs of policy are under consideration, both having level annual premiums of f1,000. Type A: 85% of the first year's premium and 101% of each subsequent premium is invested in units. On surrender the bid value of the units allocated is paid. Type B: 95% of each premium is invested in units. On surrender the bid value of the units allocated is paid less a penalty of 10% of the total premiums outstanding under the policy. There is a bid/offer spread in unit values, the bid price being 95% of the offer price. A fund management charge of 1% of the value of the policyholder's fund is deducted at the end of each policy year. The death benefit, which is payable at the end of the year of death, and the maturity value are equal to the bid value of the units allocated. Surrenders are assumed to take place at the end of the year. The office's expenses in respect of the policy are f100 at the start of the first year and f30 at the start of the second and third years. The office holds unit reserves equal to the bid value of the units and zero non-unit reserves. The dependent rate of mortality at each age is assumed to be 1% and the dependent rate of surrender at each duration is 5%. The non-unit fund is assumed to grow at the rate of 71/2% pa. (i) Calculate the unit fund values at the end of each year assuming that the growth in unit value is 71/2% pa and hence calculate the estimated maturity proceeds for each policy type. [6] (ii) Calculate the net present value of the profit that is expected to arise under each policy type, using a discount rate of 10% pa. [8] [Total 14]Question 5.1 A certain pension scheme requires its members to contribute at a rate of 692% of salary each month for a maximum period of 40 years Calculate the value of future contributions for a member now aged exactly 30 with 5 years'r past service whose earnings For the past year were 22,000. You may assume that interest rates, salary scales and decrements are the same as these underlying the pension Fund Functions in the Tables. [2] Question 5.2 The future lifetime of' a new-born person is def'med to be the random variable T , which is continuously distributed on the interval [0,50], where 0 a: a: s: cc. Assuming ELTlS {Females} mortality, calculate the Following probabilities. {a} P(rs4o|rs25) (b) P(4025) [2] Question 5.3 A level assurance policy pays a lump sum of 50,000 immediately on the death of a life aged 50, provided that he survives to his 60th birthday, and that his death occurs before that of another life currently aged 55. Derive an expression in terms of assurance functions for the expected present value of this benet, assuming that both lives are subject to the same mortality table. [4]