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

Question

BlackTom AI · Accepted Answer

Let's break down each statement about interest rates and see how compounding frequency affects them.
Option 1: 'The effective annual rate decreases as the number of compounding periods per year increases.' In reality, when positive interest is being earned, increasing the number of compounding periods per year tends to raise the effective annual rate (EAR). So this claim is incorrect because EAR typically grows with more frequent compounding rather than decreases.
Option 2: 'For any positive rate of interest, the annual percentage rate will always exceed the effective annual rate.' This goes against the standard relationship between APR and EAR. When compounding is more frequent than annually, EAR is greater than APR; only in the specific case of annual compounding do APR and EAR coincide. Therefore, this statement is not universally true and is misleading.
Option 3: 'Savers would prefer annual compounding over monthly compounding given the same annual percentage rate.' With the same APR, more frequent compounding (monthly) yields a higher EAR, which benefits the saver because they earn more interest over the year. Hence savers would generally prefer monthly compounding, making this option false.
Option 4: 'Borrowers would prefer monthly compounding over annual compounding given the same annual percentage rate.' Since monthly compounding increases the effective cost of borrowing (higher EAR), borrowers would actually prefer less frequent compounding, not monthly, at the same nominal rate. This statement is therefore incorrect.
Option 5: 'The effective annual rate equals the annual percentage rate when interest is compounded annually.' This aligns with the fundamental definition: when compounding happens once per year, EAR equals the nominal APR. This statement is correct, reflecting the standard relationship between APR and EAR under annual compounding.

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

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