an income protection policy to employed persons, which will provide the policy holders with a single payout of $40000 in the event that they become unemployed within the next two years. The premium $P for this policy would be paid at the beginning of the two year period, and the payout, if required, would occur at the end of whichever one-year period during the policy that the policy holder became unemployed. Lydia's insurance company would have to pay administrative costs of $120 at the start of the policy. The interest rate is j1=3%. Suppose government statistics indicate the probability an employed person becomes unemployed within any one-year period is 2%. Further suppose that Lydia's insurance company wishes to earn on average a net 0.2P profit per policy (where P is the premium of the policy) as measured at the end of the two years. a. [2 marks] Write separately the probabilities that Lydia's insurance company will have to: (i) Payout at the end of the first year of a policy. (ii) Payout at the end of the second year of a policy. (iii) Not have to payout a policy at all. b. [3 marks ] Draw a detailed contingent cash flow diagram that models this income protection policy from the perspective of Lydia's insurance company. c. [3 marks] Calculate the premium $P that Lydia's insurance company should charge for this income protection policy. d. [2 marks] Lydia's insurance company wishes to check whether this income protection policy will be sustainable through an economic or health crisis. Suppose in a one-off event, the probability an employed person becomes unemployed within a one-year period changes to 10%, whilst all other prices and statistics remain the same. Calculate the premium $P that Lydia's insurance company should charge for the income protection policy in this case