A bank faces two types of borrowers, A and B, both who request a $100 loan. A will repay the loan with probability 0.96 and default otherwise, while…

A bank faces two types of borrowers, A and B, both who request a $100 loan. A will repay the loan with probability 0.96 and default otherwise, while B will repay the loan with probability 0.75 and default otherwise.  The bank cannot observe type, but knows that fraction 0.65 of borrowers are type A and the rest are type B. What is the competitive pooling interest rate?

A) 16%

B) 6%

C) 21%

D) 13%

 
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