Suppose that:

(i) the premium basis is A1967-70 ultimate, 6% p.a. interest, with no allowance for expenses; and (ii) reserves are to be calculated prospectively by the gross premium method on the following basis: mortality: A1967-70 ultimate; interest: 4% p.a.; expenses: 5% of all future premiums. Find a formula for the reserve at duration t years (just before receipt of the premium then due.)6.1 (1) Express , V, in terms of A, and Ayet. Hence, or otherwise, find the values of , V, and n Vitn, given that 1 - Artin = Astin - Artn = Artn - Ar (ii) Calculate 1 Vio given that Pao = 01536, pao = .99647 and i = .05. 6.2 Consider an n-year pure endowment policy, issued to (r), with sum assured 1 and with annual premiums payable throughout the duration of the policy. In the event of death within the n years, all premiums paid will be returned without interest at the end of the year of death. Obtain expressions for the reserve at duration t (i) prospectively and (ii) retrospectively. Using commutation functions, show that your expressions are equal. (Assume that the premium due at time t has not yet been paid.) (Difficult) Given that Pr = 0.02, , V, = 0.06, and Pzah = 0.25, find Phim 6.4 Ten years ago a life office issued a 20-year endowment assurance without profits to (35). The sum assured is f10000, payable at the end of the year of death (or on survival for 20 years), and premiums are payable annually in advance. Using A1967-70 ultimate 6%, and ignoring expenses, calculate the annual premium; (ii) the reserve, assuming that the premium now due has been paid. 6.5 (Difficult) You are given: (i) P, = 0.01212 (ii) 20 Pr = 0.01508 (iii) PE:TO = 0.06942 (iv) 10 V, = 0.11430 Calculate 18VI . 6.6 A whole life assurance with sum assured f100,000 payable at the end of the year of death was purchased by a life aged 30. The policy has annual premiums payable throughout life. The basis for calculating reserves for this policy is as follows: net premium method: A1967-70 ultimate, 5% p.a. interest. Estimate the policy value at duration 28- by interpolation