A certain loan category has a 2.1% default rate and defaulted loans have a -10% return. Loans that don't default earn whatever rate the bank charges. If the lending bank wishes to earn a 4.5% average return on this loan category, including defaulted loans, what rate must the bank charge each borrower?

Question

Quizplus · Accepted Answer

To achieve an average return of 4.5%, the bank must account for the 2.1% of loans that default with a -10% return. The calculation involves setting up an equation where the weighted average of the returns from both the defaulting and non-defaulting loans equals 4.5%. Let x be the rate the bank charges. The equation is: (0.979x * 0.979) + (-0.1 * 0.021) = 0.045. Solving for x gives approximately 4.811%.

A Certain Loan Category Has a 2