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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...

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?

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