Interest rate and probability
Suppose a bank is faced with two types of borrowers (a high risk borrower that should be charged an interest rate of 9% and a low risk borrower that should be charged an interest rate of 4%). There is a 30% chance of getting a high risk borrower and a 70% chance of getting a low risk one. What is the expected interest rate that will be charged by a bank that cannot exactly distinguish between the two types but knows the probabilities of each type. In this market for loans what would be the result?