Please show all work using the Utility Theory.

BONUS PROBLEM for Utility Theory (20 points) Determine the maximum insurance premium the person would be willing to pay for a $200,000 insurance just to cover the mortgage. (Hint: in this case, the house is under-insured. In other words, with the $200,000 insurance, if the house is totally destroyed by fire, the person will suffer a loss in the net asset because the insurance covers only the mortgage not the full net equity of the house, and the maximum insurance premium the person would be willing to pay will need to be determined through numerical iterations). BONUS PROBLEM for Utility Theory (20 points) Determine the maximum insurance premium the person would be willing to pay for a $200,000 insurance just to cover the mortgage. (Hint: in this case, the house is under-insured. In other words, with the $200,000 insurance, if the house is totally destroyed by fire, the person will suffer a loss in the net asset because the insurance covers only the mortgage not the full net equity of the house, and the maximum insurance premium the person would be willing to pay will need to be determined through numerical iterations)