HTCD Bank charges an interest rate of 24.9% per annum on a loan to Evergreen Ltd. The bank also charges administration fees of 3.4% of the loan amount per annum. The compensating balance (b) is 3%, and there is 8% reserve requirement (RR). What is the contractually promised rate of return to the bank from the loan? (Instructions: Please round your answer to at least 3 decimal places. Keep more decimal places if your answer is small. Please also keep your answer in decimals not percentage terms.)数值题
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Question

HTCD Bank charges an interest rate of 24.9% per annum on a loan to Evergreen Ltd. The bank also charges administration fees of 3.4% of the loan amount per annum. The compensating balance (b) is 3%, and there is 8% reserve requirement (RR). What is the contractually promised rate of return to the bank from the loan? (Instructions: Please round your answer to at least 3 decimal places. Keep more decimal places if your answer is small. Please also keep your answer in decimals not percentage terms.)数值题

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BlackTom AI · Accepted Answer

To determine the contractually promised rate of return, I will break down the components and clarify what counts toward the bank's earnings versus what limits its earnings power.
First, identify the bank's income components from the loan: the interest paid by Evergreen Ltd at 24.9% per year, and the administration fees at 3.4% of the loan amount per year. Together, these produce 0.249 + 0.034 = 0.283 of loan amount per year in gross income for the bank.
Next, account for the resources that are not available to the bank to generate income: not only does the bank have to hold a compensating balance of 3% of the loan (b = 0.03) in the borrower's account, but it also must hold reserves equal to 8% of the loan (RR = 0.08). These amounts effectively reduce the bank’s usable funds that can be deployed to earn the stated income. Hence, the total deduction from the loan amount for calculating the return is 0.03 + 0.08 = 0.11, leaving 1 - 0.11 = 0.89 of the loan amount as the net funds effectively earning the stated income.
Now, compute the contractually promised rate of return as the annual income (0.283 L) divided by the net funds deployed (0.89 L): 0.283 / 0.89 ≈ 0.317977978. Rounding to at least three decimal places, the value is approximately 0.317978.
For completeness, note the alignment of the components: the numerator captures all bank earnings from the loan (interest plus fees), while the denominator represents the actual amount of funds the bank can use to generate those earnings after accounting for the compensating balance and reserve requirements. Any alternative view that ignores reserves or compensating balances would misstate the bank’s true return on the loan.
Thus, the contractually promised rate of return to the bank from the loan, expressed as a decimal, is about 0.317978.

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