Tom is a farmer with a utility function of U = I^0.5, where U is Tom's utility and I is his income. If the weather is good, he will earn $100,000. If there is a hailstorm, he will earn only $50,000. The probability of a hailstorm in any given year is 30%.

What is Tom's expected income if he is insured?

What is Tom's expected utility if he is insured? (Round up to 2 decimal places)

Suppose a crop insurer makes the following offer to Tom: in years when there is no hailstorm, Tom pays the insurer $16,000. In years when there is a hailstorm, the insurer pays Tom $34,000.

What is Tom's expected income?

What is Tom's expected utility? (Round up to 2 decimal places)

Suppose instead the insurer makes the following offer to Tom: in years when there is no hailstorm, Tom pays the insurer $10,000. In years when there is a hailstorm, the insurer pays Tom $20,000.

What is Tom's expected income?

What is Tom's expected utility?

2.

Suppose that when you were one year old, your grandmother gave you $100. Your parents put $100 in a savings account with a guaranteed 9% interest rate, and then promptly forgot about it

Use the Rule of 72 to estimate how much that account will grow to by the time you are 65. (Round up to 2 decimal places)

Calculate exactly how much you will have in that account using the formula for compounding interest. (Round up to 2 decimal places)

*Please show the graphs and how to find this data