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A lender offers $220 loans and their are two types of borrowers, A & B. Type...

A lender offers $220 loans and their are two types of borrowers, A & B. Type A repays 100% of the time and B repays 85% of the time. The lender offers a loan and cannot tell which type of borrower he faces, but figures the probability the borrower is type A is 60%. Find the mark-up type A pays on her interest rate, where the mark up is defined as the difference between what she would pay if the bank knew her type and what she pays in the pooling contract? Please explain, thank you!

A 9.9%
B) 6.4%
C) 5.2%
D) 4.1%

Solutions

Expert Solution

Solution

Total repayment probability = (1*0.60)+(0.85*0.40) = 0.94

Pooling interest rate = (1/ total repayment probability) -1

Pooling interest rate = (1/0.94)-1= 0.638 or 6.38%

Option B is correct 6.4%

jeff jeffy answered 2 years ago
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