A person has a total net asset of $1 million, including a $200,000 net equity of a house, which is the market value of the house (structure and land values) mortgage. Specifically, the house has a market value of $500,000, a structure value of $400,000, a land value of $100,000, and a mortgage of $300,000. The person plans to buy $400,000 fire insurance for full coverage of the house. For simplicity, assume that each year the house has a 1% probability of being totally destroyed by fire and a 99% probability of no damage occurring to the house. Furthermore, the persons utility for money is approximately proportional to the cubic root of money and U($1000,000)=10 and U($0)=0. B1.(5 points) Draw the decision tree for the insured about buying or not buying the fire insurance. B2.(10 points) Determine the maximum insurance premium IP the person would be willing to pay. B3. (5 points) What is the risk premium at the maximum IP? Bonus Problem (20 points). Determine the maximum insurance premium the person would be willing to pay for a $300,000 insurance just to cover the mortgage (Hint: in this case, even insured, if the house is destroyed, the person will suffer a loss in net asset in addition to paying for the insurance premium, and the highest insurance premium needs to be determined through numerical iteration).