When is the EAR equal to the annual nominal rate?

The effective annual rate (EAR) is equal to the annual nominal rate specifically when compounding occurs annually. This is due to the nature of compounding itself. When interest is compounded annually, the interest that accrues is added to the principal once per year, which means that there is no additional compounding effect throughout the year. Therefore, the nominal interest rate and the effective rate are the same because there are no additional periods in which interest could accumulate.

In contrast, when interest is compounded more frequently (monthly, quarterly, or daily), the effective annual rate will always be higher than the nominal rate. This is because each time interest is compounded, it adds to the principal, which leads to interest being earned on previously accrued interest, thus increasing the overall yield over the year. Consequently, the frequency of compounding has a significant impact on the effective annual rate, emphasizing how compounding more than once a year results in a higher ear compared to simply applying the nominal rate once per year.