City Bank wants to appear competitive based on quoted loan rates and thus must offer a 7.75 percent annual percentage rate on its loans.What is the maximum rate the bank can actually earn based on the quoted rate?

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Quizplus · Accepted Answer

The maximum rate the bank can actually earn based on the quoted rate is calculated by considering the effect of compounding. Since the quoted rate is 7.75 percent as an annual percentage rate (APR), if the bank compounds interest more frequently than annually, it can earn more than the quoted rate. The effective annual rate (EAR) can be calculated using the formula EAR = (1 + APR/n)^n - 1, where n is the number of compounding periods per year. To maximize the rate, the bank would compound as frequently as possible, theoretically an infinite number of times, leading to continuous compounding. Using continuous compounding, the formula becomes EAR = e^(APR) - 1, where e is the base of the natural logarithm, approximately 2.71828. However, without specifying the compounding frequency, we can't directly calculate the exact maximum rate. Among the given options, 8.06 percent is the closest to what could be achieved with frequent compounding (e.g., daily or monthly) without exceeding realistic banking practices. Therefore, without the exact compounding frequency or applying continuous compounding directly, we choose the option that represents a reasonable increase over the APR due to compounding.

City Bank Wants to Appear Competitive Based on Quoted Loan