Assignment task: John's utility function for money is the cubic or third root of the amount of money. Specifically, for John, U($1,000,000)=100 and U($0)=0. John has a net asset of $20,000,000, including a house with a structural value of $6,000,000. Based on annual fire statistics, each year John's house structure has a 1% probability of being totally destroyed by fire, a 5% probability of being 50% destroyed by fire, and a 94% probability of nothing happening to the structure. Based on these data, use the decision tree analysis to compute:
1. The maximum Insurance Premium (IP) that John will be willing to pay for fully insuring the structure for $6,000,000.
2. The Risk Premium he will pay for fully insuring the structure for $6,000,000.
To minimize roundoff errors, all numbers should carry 4 digits after the decimal point.