Which one of the following statements concerning interest rates is correct?

Question

BlackTom AI · Accepted Answer

Let's walk through each statement carefully and compare them to the concept of the effective annual rate (EAR) and the annual percentage rate (APR).
Option A: 'Savers would prefer annual compounding over monthly compounding given the same annual percentage rate.' In reality, with the same APR, more frequent compounding (e.g., monthly) yields a higher EAR, which benefits savers. So this claim is incorrect because it ignores the fact that EAR rises with more compounding periods.
Option B: 'The effective annual rate decreases as the number of compounding periods per year increases.' This is the opposite of how EAR behaves. As compounding frequency increases, EAR increases (it approaches the nominal rate adjusted for compounding). Therefore, this statement is false.
Option C: 'The effective annual rate equals the annual percentage rate when interest is compounded annually.' When compounding is annual, there is no difference between EAR and APR—the two rates coincide. This statement is correct because EAR = APR under yearly compounding.
Option D: 'For any positive rate of interest, the annual percentage rate will always exceed the effective annual rate.' This is incorrect because when compounding more than once per year, the EAR is greater than the APR; only in special cases with zero or no compounding does EAR equal APR, but not generally. So this option misstates the relationship between APR and EAR.
Option E: 'Borrowers would prefer monthly compounding over annual compounding given the same annual percentage rate.' Borrowers would actually face higher interest costs with more frequent compounding (higher EAR) at the same APR, all else equal, so they would not necessarily prefer monthly over annual. This makes the statement false.
In summary, the only statement that aligns with the standard relationship between APR and EAR across compounding frequencies is Option C, which correctly notes that EAR equals APR when compounding is annual.

Which one of the following statements concerning interest rates is correct?单项选择题

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