Effective Annual Rate

A 12% annual interest rate on a loan or savings account rarely means you pay or earn exactly 12% per year. Compounding often makes the real cost or yield higher. That true annual percentage is the effective annual rate (EAR). Understanding EAR is essential when comparing financial products that compound interest at different frequencies.

What Is the Effective Annual Rate?

The effective annual rate (also called the effective interest rate or annual equivalent rate) is the actual annual interest rate after accounting for compound interest over one year. It tells you what the year-end balance will be relative to the starting principal, assuming all interest is reinvested or charged at the same rate.

A nominal annual rate ignores intra-year compounding. EAR corrects for that by converting the stated rate into a true annual measure. For example, a nominal 10% rate compounded semi‑annually produces an EAR of 10.25%, not 10%.

How Do You Calculate the Effective Annual Rate?

The standard formula for EAR is:

Where:

• \(i\) – nominal annual interest rate (as a decimal)
• \(n\) – number of compounding periods per year

Example: A nominal rate of 12% compounded monthly (n = 12).

Even though the advertised rate is 12%, the effective annual rate is 12.68%. The difference comes from earning interest on interest each month.

You can quickly find the EAR for any nominal rate and compounding schedule using the calculator below. Enter the stated annual rate and select how often interest is compounded. The tool applies the formula instantly.

How Does Compounding Frequency Affect the Effective Annual Rate?

For the same nominal rate, more frequent compounding always increases the EAR – though the gains diminish as frequency becomes very high.

Continuous compounding uses the formula \(\text{EAR} = e^{i} - 1\), where \(e \approx 2.71828\). The difference between daily and continuous compounding is minimal – only about 0.001 percentage points at 10%.

What’s the Difference Between EAR, APR, and APY?

These terms overlap but are not interchangeable:

• Effective Annual Rate (EAR) – purely the annualized effect of compound interest, excluding fees.
• Annual Percentage Yield (APY) – used for deposit and savings products; essentially the same as EAR, reflecting compounding.
• Annual Percentage Rate (APR) – a broader cost measure that may include fees and often does not incorporate compounding in the advertised rate. For credit cards in the U.S., APR is a nominal rate applied daily, so the effective rate will be higher than the stated APR.

When comparing loans or credit cards, look at the EAR or the effective rate based on the periodic rate. For savings accounts, use APY – it’s the effective annual rate.

When Should You Use the Effective Annual Rate?

• Comparing loan offers: Two loans might have the same nominal rate but different compounding frequency. EAR shows which one costs more.
• Evaluating investment returns: A bond paying 5% semi‑annually yields a 5.06% effective annual rate. Use EAR to measure real growth.
• Credit card balances: Daily compounding makes the effective annual rate significantly higher than the nominal APR.
• Regulatory disclosures: In the European Union, the Annual Equivalent Rate (AER) is the effective annual rate for savings products.

Investors and borrowers who ignore compounding can misjudge costs by over 0.5 percentage points or more on typical high‑yield products.

This article provides general information and does not constitute financial advice. Check current rates and terms with your financial institution before making decisions.