Suppose a bank is faced with two types of borrowers- a high risk borrower that s

Question

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?

Explanation / Answer

.09*.3+ .7*.04 = .55

interest rate charges = .55 i.e 5.5%

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