My current wealth is $1000 and I have exponential utility with a=0.001. There is a 2% chance that my basement will start leaking next week, in which case I will have to spend $500 to fix the problem. I am offered an insurance contract that costs c today, and will pay for any future repairs in the event it does start leaking. (a) What is my utility if I do not purchase the insurance and my roof does not leak? (b) What is my utility if I do not purchase the insurance and my roof does leak? (c) What is my utility if I purchase the insurance? (d) Should I purchase the insurance if c = 6.45? (e) What is the maximum price that I should be willing to pay for the insurance? Please round your answer to the nearest cent.