I Question 5 [20 marks]. [4] (a) Dan Brown, aged 55, takes out a whole-life assurance policy with a sum insured of 100,000 paid at end of year of death. Assume an effective interest rate of 4% per annum and mortality given by the AMC00 Select Table. () Show that the cost of the life assurance policy as a net single premium is approximately 36,297. (ii) If he pays for the assurance annually in advance for life, what is the annual premium? (iii) If he instead pays for the assurance by making quarterly payments for life in arrears, what is the quarterly premium? (b) Consider a life assurance policy for a life of age x, in which a 1 death benefit is paid at the instant of death, but only if death occurs within n years from the start of the contract. Determine an expression for the expected present value of such a policy assuming that the complete further lifetime T(x) is uniformly distributed on the interval (0,0 - x). where 6 >O is a constant, and 0O is a constant, and 0