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Answer: 2.24%
## Explanation The bank's formula for setting the interest rate on loans is: **Interest rate = Expected loss + Margin for profit and OpEx + Funding cost** Using the given values: - Average interest rate on loans = 8.18% - Margin for profit and operating expenses = 2.10% - Average funding cost = 4.85% We can calculate the expected loss: **Expected loss = 8.18% - 2.10% - 4.85% = 1.23%** The expected loss formula is: **Expected loss = Probability of default × Loss given default** Where: - Loss given default = 1 - Recovery rate - Recovery rate = 45% - Loss given default = 1 - 45% = 55% Therefore: **Probability of default = Expected loss ÷ Loss given default** **Probability of default = 1.23% ÷ 55% = 2.2364% ≈ 2.24%** This matches option C.
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A small bank sets the interest rates it charges on loans to its business clients at a level equal to the sum of the loans' expected loss, the bank's funding cost, and a margin for the bank's profit and operating expenses. A risk analyst at the bank compiles the following information related to the loan portfolio:
| Average recovery rate of loans | 45% |
|---|---|
| Margin for profit and operating expenses | 2.10% |
| Average funding cost | 4.85% |
| Average interest rate on loans | 8.18% |
Given this information, what is the estimated average probability of default for the loans in the portfolio?
A
0.68%
B
1.23%
C
2.24%
D
2.73%
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