(a) A life office sells an endowment insurance to a life aged 40 with a term of 25 years. Use AM92 ultimate mortality to calculate the single premium and variance of the present value of benefits. The sum insured is $100,000 and interest is assumed to be at 4% per annum. (4 marks) (b) A life office sells n identical and independent policies as in (a). It will charge the premium calculated in (a) plus a loading of 2% to cover variability in experience. Calculate the number of policies the office must sell if it is to have a no larger than 1% chance of making a loss on this business. [Hint: The expected present value of the profit is the premium charged with loading minus the premium charged without loading. Zo.95-1.645, Z0.975-1.96, Z0.99=2.3263.] (7 marks)