Effective annual rate (EAR) is ………… annual percentage rate (APR) when interest is paid many times a year.

Question

BlackTom AI · Accepted Answer

When comparing EAR and APR, it's important to recall how compounding frequency affects the effective rate. 
Option 1: 'None of the above' would be incorrect because there is a clear relationship between EAR and APR when compounding occurs multiple times per year. The statement is not accurate in this context. 
Option 2: 'Equal to' is not generally true unless interest is compounded exactly once per year. Since interest is paid many times a year in the scenario, EAR will diverge from APR. 
Option 3: 'Greater than' reflects the standard result: if interest is compounded more frequently than annually, the EAR exceeds the quoted APR because interest accrues on interest within each year, effectively boosting the annual yield. This aligns with the mathematical definition of EAR = (1 + APR/m)^{m} − 1 for m > 1, which yields a value above APR itself. 
Option 4: 'Less than' would be incorrect because more frequent compounding cannot reduce the effective annual rate below the nominal APR; the compounding effect increases the total growth within the year. 
In summary, only the statement asserting that EAR is greater than APR when interest is paid multiple times a year is consistent with standard time value of money principles and the formula for EAR under periodic compounding.

Effective annual rate (EAR) is ………… annual percentage rate (APR) when interest is paid many times a year.单项选择题

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