A risk averse individual with a wealth of 156,000 and utility function U(x) = sqrt(x) is considering whether to purchase fire insurance for their home. The probability of a fire is 0.03. Repairing the damage from a fire costs 96,000. A risk neutral insurance company offers a fire insurance policy that fully insures the policy holder.
What is the maximum amount that the insurance company can charge the individual for a policy that fully insures them against the risk of a fire? ?