Lydia works for an insurance company. Her company wishes to provide an income protection policy to employed persons, which will provide the policy holders with a single payout of $10 000 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 $60 at the start of the policy. The interest rate is j1 = 9%. Suppose government statistics indicate the probability an employed person becomes unemployed within any one-year period is 1%. Further suppose that Lydia’s insurance company wishes to earn on average a net 0.05P profit per policy (where P is the premium of the policy) as measured at the end of the two years.

 a. 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. Draw a detailed contingent cash flow diagram that models this income protection policy from the perspective of Lydia’s insurance company.

c. Calculate the premium $P that Lydia’s insurance company should charge for this income protection policy.