$5.(3$ points$)$ Calculate the actuarial fair premium $($AFP$)$ for the full coverage quoted by Country Land Insurance Company.

$6.(8$ points$)$ Would you be better off purchasing the coverage quoted at the AFP than purchasing no insurance? Support your answer with Utility Theory.

$7.(8$ points$)$ Calculate the premium load that Country Land Insurance Company could add to the AFP for full coverage such that you would be indifferent between purchasing the coverage and retaining the risk yourself. Express the load both in dollar terms and as a percentage of the AFP.

$8.(4$ points$)$ You are interested in reducing your premium through coinsurance. Calculate your updated actuarial fair premium $($AFP$)$ for the policy with $25\%$ coinsurance, assuming no change in your loss distribution.