Answer the questions below with explanations

(i) Express . V, in terms of A, and Aret. Hence, or otherwise, find the values of , V, and nVren, given that 1 - Artin = Art2n - Artn = Artn - Ar (ii) Calculate 1V40 given that Plo = .01536, po = .99647 and i = .05. Consider an n-year pure endowment policy, issued to (x), with sum assured 1 and with annua premiums payable throughout the duration of the policy. In the event of death within the 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, nVr = 0.06, and Prim = 0.25, find Prim . 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 (i) the annual premium; (ii) the reserve, assuming that the premium now due has been paid. (Difficult) You are given: (i) Pr = 0.01212 (ii) 20 Pr = 0.01508 (iii) Pr:10 = 0.06942 (iv) 10Vr = 0.11430 Calculate 10 20 Vr . 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. Describe the following terms briefly: (i) net premium reserves; Zilly(iii) Full Preliminary Term reserves; and (iv) gross premium reserves, in each case giving suitable formulae in respect of a whole life assurance issued t years ago a life then aged r, with level premiums payable annually in advance throughout the term an with a sum assured of El payable at the end of the year of death. Assume that the premium now due has not yet been paid