What is the formula for the effective annual rate when interest is compounded m times per year with nominal rate i?

• A. EER = i
• B. EER = (1 + i/m)^m - 1
• C. EER = (1 + i)^m - 1
• D. EER = i/m

Answer: (B)

When you have a nominal annual rate i with m compounding periods per year, the interest earned in each period is i/m. Over a full year, you accumulate growth of (1 + i/m) for each of the m periods, so the total factor is (1 + i/m)^m. Subtracting 1 gives the effective annual rate: (1 + i/m)^m - 1. This captures the true yearly yield because it accounts for interest-on-interest inside the year. For example, with i = 0.12 and m = 12, the effective rate is (1 + 0.12/12)^12 - 1 ≈ 0.1268, or about 12.68%. The other forms misrepresent the concept: i alone ignores intra-year compounding, i/m is just the per-period rate, and (1 + i)^m assumes the full annual rate is applied every period.