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 $40 000 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 $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.