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. Lydias 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 Lydias 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.

Lydias 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 Lydias insurance company should charge for the income protection policy in this case.