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Qu ESTIDN 1 [11] marks] Lydia works for an insurance company. Her oompany wishes to provide an income protection policy to employed persons1 which will provide the policy holders with a single payout of $4GDUG in the event that they become unemployed within the next two years. The premium $13 for this policy would be paid at the beginning of the two year period, and the payout, if required1 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 jl = 3%. Suppose govermnent statistics indicate the probability an employed per son becomes unemployed within any oneyear period is 2%. Further suppose that Lydia's insurance company wishes to earn on average a net H.213 prot per policy [where P is the premium of the policy} as measured at the end of the two years. a. [2 marks] 1'ql'm'rite separately the probabilities that Lydia's insurance com pany will have to: (i) Payout at the end of the rst 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. h. [3 marks] Draw a detailed contingent cash ow diagram that models this income protection policy from the perspective of Lydia's insurance company. c. [3 marks] Calculate the premium $P that Lydials insurance company should charge for this income protection policy. d. [2 marks] Lydials insurance company wishes to check whether this in come protection policy will he sustainable through an economic or health crisis. Suppose in a oneoff event1 the probability an employed person becomes unemployed within a oneyear period changes to 109331 whilst all other prices and statistics remain the same. Calculate the premium $P that Lydials insurance company should charge for the income protection policy in this case