A bank can issue a $200 loan to a borrower. The buyer can be two different types

Question

A bank can issue a $200 loan to a borrower. The buyer can be two different types, and the bank cannot observe this. If the borrower is type x, she will repay with probability 0.96 and default with probability 0.05. If she is type y, she will repay with probability 0.75 and default otherwise. Assume half of the borrowers are of each type. What is the minimum interest rate the bank must charge to make lending worthwhile? 0.24 0.22 0.17 0.14 Consider the credit market in question 4 again. What is the additional risk premium that type x must pay (over what her own risk premium is), when she is pooled together with type y in the loan contract? 0.13 0.16 0.19 0.20

Explanation / Answer

I am answering assuming the probability of 'x' repalying is 0.95 & not 0.96

a. Combining 'x' & 'y' the probability of default is 0.025 + 0.125 = 0.15

i.e. for every $100 lent by the bank $85 will be repaid, so on these $85 they need to charge a minimum interest of $15 =15/85 = 17.64 % 0.17....option c.

b. Considering on 'x' scenario: probability of default is 0.05, solving as above minimum of $5 will be charged on $95 = 5/95 = 5.2 %.

So by combining 'x' need to pay an aditional risk premium of 17.64 - 5.2 = 12.44% 0.13 ....option a.

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