Roulan Has Wealth of $40,000 as Long as His Business

Multiple Choice

Roulan has wealth of $40,000 as long as his business does not burn down. However, there is a 50% probability that his business will burn down, causing a loss of $30,000 and leaving him with $10,000 of wealth. Roulan's utility function is given by U = W^0.5, where W is wealth. Suppose Roulan purchases insurance to cover the potential $30,000 loss. If the insurance premium is actuarially fair, Roulan's utility with insurance is:

A) 100.40.
B) 145.23.
C) 158.11.
D) 161.51.