Rafael needs a loan of $1,000. A bank figures that he will default with probabil
ID: 2468229 • Letter: R
Question
Rafael needs a loan of $1,000. A bank figures that he will default with probability 0.09, or 9%. If Rafael can increase his credit score he can reduce this to 6%. What would the change in interest rate be if the rates are competitive? a. 2% b. 3% c. 5% d. 11% 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? a. 0.24 b. 0.22 c. 0.17 d. 0.14Explanation / Answer
Answer 3.
Risk free rate - 1.67%
Interest rate with the credit score 9% = Risk free rate + Beta (i.e. Risk free rate*Probabiliity of default)
= 1.67+1.67(9%)
= 1.82%
Interest rate with the credit score 6% = Risk free rate + Beta (i.e. Risk free rate*Probabiliity of default)
= 1.67+1.67(6%)
= 1.77%
% Change in interest rate= 1.82-1.77 i.e. 5%
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