If the effective annual interest rate is 6%, what is the nominal rate or APR (Annual Percentage Rate), given monthly compounding?

Question

BlackTom AI · Accepted Answer

The problem asks us to convert an effective annual rate (EAR) of 6% to a nominal annual rate (APR) with monthly compounding.

To relate EAR to a monthly-compounded nominal rate, use the formula (1 + APR/12)^{12} = 1 + EAR. Here, EAR = 0.06, so we solve (1 + APR/12)^{12} = 1.06.

Let x = APR/12. Then (1 + x)^{12} = 1.06. Taking the 12th root gives 1 + x = 1.06^{1/12}, so x = 1.06^{1/12} − 1.

Therefore APR = 12x = 12[1.06^{1/12} − 1]. Using a calculator, 1.06^{1/12} ≈ 1.004867, so x ≈ 0.004867, and APR ≈ 12 × 0.004867 ≈ 0.0584, i.e., about 5.84%.

Thus, among the provided option, the portion labeled 5.84% aligns with the mathematical relationship between EAR and a monthly-compounded APR for a 6% effective annual rate.

Note: If there were additional options, we would compare them against the same derivation, checking for consistency with the formula (1 + APR/12)^{12} = 1.06 and ensuring any alternative numbers reflect the correct annualization under monthly compounding.

If the effective annual interest rate is 6%, what is the nominal rate or APR (Annual Percentage Rate), given monthly compounding?

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