Which statement about APR and monthly rates is correct?

Study for the Finance and Investment Challenge Test. Approaches include flashcards and multiple-choice questions with hints and explanations. Ready yourself to ace the exam!

Multiple Choice

Which statement about APR and monthly rates is correct?

Explanation:
When you convert a monthly interest rate to an annual rate, you multiply by 12 if you’re using the simple, or nominal, annual rate. If the rate is r per month, r × 12 gives the annual rate in a straightforward way and is what APR often represents when compounding within the year is not considered. This is why APR is described as the annualized version of the monthly rate in many contexts. It’s useful to note the caveat: if you account for compounding, the true yield would be (1 + r)^12 − 1, which is a bit higher than r × 12. For example, with a monthly rate of 0.5% (r = 0.005), the nominal APR would be 0.005 × 12 = 6%, while the effective annual rate would be (1.005)^12 − 1 ≈ 6.17%. So the statement that APR equals the monthly rate times 12 reflects the simple annualization approach and is the best-fit description in that context.

When you convert a monthly interest rate to an annual rate, you multiply by 12 if you’re using the simple, or nominal, annual rate. If the rate is r per month, r × 12 gives the annual rate in a straightforward way and is what APR often represents when compounding within the year is not considered. This is why APR is described as the annualized version of the monthly rate in many contexts.

It’s useful to note the caveat: if you account for compounding, the true yield would be (1 + r)^12 − 1, which is a bit higher than r × 12. For example, with a monthly rate of 0.5% (r = 0.005), the nominal APR would be 0.005 × 12 = 6%, while the effective annual rate would be (1.005)^12 − 1 ≈ 6.17%.

So the statement that APR equals the monthly rate times 12 reflects the simple annualization approach and is the best-fit description in that context.

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