A customer has approached a bank asking for $50,000 one year loan that the bank would make at 12% interest on. If the bank does not issue the loan, the bank will invest the $50,000 in some corporate bonds that earn a 6% annual return. Without further information, the bank believes that there is a 4% chance that the customer will totally default on the loan. If the customer totally defaults the bank would lose the %50,000 completely. At a cost of $500, the bank can pay a credit agency to do a credit check.
The credit agency will supply a favourable or unfavourable recommendation. Past experience indicates that with a favourable recommendation there is a 98% chance that the customer does not default and 2% chance the customer defaults. Use a decision tree to show how the bank can maximize their expected profits.