1. A bank charges 10% on a loan to a firm that has a 5% probability of default. If the firm defaults, then the bank expects to recover 50% of what is owed.

a. What is the expected return on this loan?

b. Suppose that the risk-free rate is 7.50%. The bank has imposed an interest rate cap of 10% on its loans. What would be the maximum default probability such that this firm could qualify for this loan?