5. [8 marks] Let's assume that we have a portfolio of 100 whole life insurance policies. You are also given the following information: each of the 100 lives, all currently age x, are independent each of the 100 lives are subject to a constant force of mortality, u = 0.02 for each policy, a death benefit of 50 is payable at the moment of death the death benefit payments are withdrawn from an investment fund that earns 8 = 0.04 . . Calculate the minimum amount needed in the fund, at time t = 0, such that there is a 95% chance that sufficient funds will be on hand to withdraw the benefit payment upon the death of each individual. (Hint: Use the Central limit Theorem here with 20.95 = 1.645). Note: I am looking for the total amount needed in the fund at time 0, NOT the amount needed from each member in the portfolio. 5. [8 marks] Let's assume that we have a portfolio of 100 whole life insurance policies. You are also given the following information: each of the 100 lives, all currently age x, are independent each of the 100 lives are subject to a constant force of mortality, u = 0.02 for each policy, a death benefit of 50 is payable at the moment of death the death benefit payments are withdrawn from an investment fund that earns 8 = 0.04 . . Calculate the minimum amount needed in the fund, at time t = 0, such that there is a 95% chance that sufficient funds will be on hand to withdraw the benefit payment upon the death of each individual. (Hint: Use the Central limit Theorem here with 20.95 = 1.645). Note: I am looking for the total amount needed in the fund at time 0, NOT the amount needed from each member in the portfolio