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A bank faces two types of borrowers, type A and B. Both want a $355 loan. Type A repays the loan 100% of the time

A bank faces two types of borrowers, type A and B. Both want a $355 loan. Type A repays the loan 100% of the time and type B only repays with probability 0.88. The bank doesn't observe type, but believes fraction z is type A. What does z need to be so that the bank can afford a pooling interest rate of 4%?

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