What is the Effective Annual Rate (EAR)?

EAR is the true annual interest rate that accounts for the effect of compounding within a year. It is calculated as (1 + r/n)^n − 1, where r is the nominal rate and n is the number of compounding periods.

Is EAR the same as APY?

Yes, functionally EAR and APY are calculated with the same formula. APY is the term banks use for savings products; EAR is the term used in academic and professional finance.

Why does EAR matter for comparing financial products?

EAR standardizes products with different compounding frequencies so you can compare them directly. A lower nominal rate compounded more frequently can have a higher EAR than a higher nominal rate compounded less frequently.

Effective Annual Rate (EAR): Formula and Calculator

What is the Effective Annual Rate?

The Effective Annual Rate (EAR), also called the Annual Equivalent Rate (AER) or Effective Annual Interest Rate (EAIR), is the true annual interest rate that accounts for the effect of compounding over a given year. When interest is compounded more than once per year, the actual return or cost exceeds the stated nominal rate — and the EAR is the figure that accurately represents this true annual impact.

EAR is the answer to the question: "What single annual rate, applied once at the end of the year, would produce the same outcome as this nominal rate compounding n times per year?" It is the unified measure that allows fair comparison across financial products with different compounding structures.

The EAR Formula

EAR = (1 + r/n)ⁿ - 1

r = Nominal annual interest rate (as a decimal)
n = Number of compounding periods per year

The result is expressed as a decimal; multiply by 100 to convert to a percentage.

Step-by-Step EAR Calculation

Example: A savings account offers 6% nominal rate, compounded quarterly.

Step 1: Identify variables: r = 0.06, n = 4

Step 2: Calculate r/n: 0.06/4 = 0.015

Step 3: Add 1: 1 + 0.015 = 1.015

Step 4: Raise to the nth power: 1.015⁴ = 1.06136

Step 5: Subtract 1: 1.06136 - 1 = 0.06136

Step 6: Convert to percentage: 0.06136 × 100 = EAR = 6.136%

The nominal rate is 6%, but you actually earn 6.136% because quarterly compounding adds extra growth during the year. On $10,000, this means earning $613.60 instead of $600.00 — a difference of $13.60 that compounds in future years.

EAR Across Different Compounding Frequencies

Using a nominal rate of 6% (r = 0.06):

Annually (n=1): EAR = (1 + 0.06/1)¹ - 1 = 6.000%
Semi-annually (n=2): EAR = (1 + 0.06/2)² - 1 = 6.090%
Quarterly (n=4): EAR = (1 + 0.06/4)⁴ - 1 = 6.136%
Monthly (n=12): EAR = (1 + 0.06/12)¹² - 1 = 6.168%
Daily (n=365): EAR = (1 + 0.06/365)³⁶⁵ - 1 = 6.183%
Continuous: EAR = e^0.06 - 1 = 6.184%

The entire range from annual to continuous compounding spans only 0.184 percentage points at 6%. The law of diminishing returns is clearly visible — each increase in compounding frequency adds less than the previous one.

EAR for High-Rate Products: Where It Really Matters

At low nominal rates, the difference between nominal rate and EAR is modest. At high rates — like those on credit cards and short-term loans — the gap becomes significant.

Credit card at 24% APR, compounded daily: EAR = (1 + 0.24/365)³⁶⁵ - 1 = 27.11%. You pay 3.11 percentage points more than the advertised rate.
Store card at 29.99% APR, compounded daily: EAR = 34.96%. Nearly 35% effective annual cost.
Payday loan at 400% APR: EAR compounds to an astronomical figure — effectively several times the principal in fees if held for an extended period.

Understanding EAR on high-rate debt makes the urgency of eliminating it obvious. A 27% EAR means your debt grows by 27% per year if not actively repaid — a compounding rate that exceeds virtually any investment return you could realistically earn.

EAR vs APY: Are They the Same?

Functionally, EAR and APY are calculated using the same formula and produce the same result. The terminology differs by context and convention:

APY (Annual Percentage Yield) is the term used by banks and financial institutions for consumer savings products (savings accounts, CDs, money market accounts). Regulated under the Truth in Savings Act in the U.S.
EAR (Effective Annual Rate) is the term used in academic finance, corporate finance, and professional investment analysis contexts.
AER (Annual Equivalent Rate) is the equivalent term used in the United Kingdom.

When a bank tells you their savings account earns 5.12% APY and you calculate EAR for the same product, you will get 5.12%. They are the same concept with different names in different contexts.

Using EAR to Compare Financial Products

The practical value of EAR is as a standardization tool. When comparing products with different nominal rates and different compounding frequencies, converting each to EAR allows a direct apples-to-apples comparison.

Example comparison:

Bank A: 5.00% nominal, compounded monthly → EAR = 5.116%
Bank B: 5.10% nominal, compounded annually → EAR = 5.100%
Bank C: 4.95% nominal, compounded daily → EAR = 5.073%

Bank A has the lowest stated rate but the highest EAR, making it the best choice for savers despite the seemingly lower nominal rate. Without converting to EAR, you might mistakenly choose Bank B based on its higher nominal rate.

EAR for Continuous Compounding

In the limit of continuous compounding — where interest is compounded at every instant — the EAR formula becomes: EAR = e^r - 1

Where e ≈ 2.71828 (Euler's number). For r = 0.06: EAR = e^0.06 - 1 = 6.184%. This is the theoretical maximum EAR achievable for a 6% nominal rate, and daily compounding (6.183%) achieves 99.99% of this maximum.

Conclusion

The Effective Annual Rate is the definitive measure for comparing financial products with different compounding structures. Whether evaluating savings accounts, loans, credit cards, or investment products, converting nominal rates to EAR ensures you are comparing actual annual costs and returns — not nominal figures that can be misleading. Use our compound interest calculator to explore how different rates and compounding frequencies translate into real-dollar outcomes for your specific balance and time horizon.