A customer has apprached a bank for $20,000 one-year loan at a 18% interest rate. If the bank does not approve this loan application the $20,000 will be invested in bonds that earn a 5% annual return. The bank will charge the customer an up-front $200 legal fee if the loan is granted. The bank believes that there a p% chance that this customer will default on the loan, assuming that the loan is approved. If the customer defaults on the loan tha banl will lose $10,000. Should the bank make the loan?..
If the objective is to maximize the bank's profit, what is the smallest value of p for the which the bank should not grant the loan? (Obviously as p decreases, the profitability of the loan increases.) Explain