Effective Annual Rate (EAR) Calculator
Convert a nominal interest rate to the effective annual rate (EAR) to find the true annual cost of a loan or the real return on an investment when compounding is applied. Supports daily, monthly, quarterly, and other compounding periods.
How to use this tool
- Enter nominal annual interest rate and compounding periods per year in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your effective annual rate (ear) and the full breakdown beneath it.
⚠ This tool provides general estimates for education only and is not financial, tax or legal advice. Figures may not reflect your situation — verify with a qualified professional.
Formula
EAR = (1 + r/n)n − 1
Where r is the nominal annual rate (as a decimal) and n is the number of compounding periods per year.
The periodic rate is r / n.
How it works
The effective annual rate accounts for the compounding of interest within the year, converting any nominal rate and compounding frequency into a single comparable annual figure. Because interest earned in earlier periods itself earns interest in later periods, EAR always equals or exceeds the nominal rate. It is identical to Annual Percentage Yield (APY) as defined by US banking regulations.
Worked example
Monthly Compounding on a 12% Nominal Rate
- Nominal rate r = 12% = 0.12; compounding periods n = 12 (monthly).
- Periodic rate = 0.12 / 12 = 0.01 (1% per month).
- EAR = (1 + 0.01)^12 − 1 = 1.126825... − 1 = 0.126825.
- EAR = 12.6825% vs 12% nominal — a spread of 0.6825%.
The effective annual rate is 12.6825%, which is 0.6825% higher than the stated 12% nominal rate.
Common mistakes to avoid
- Entering the nominal rate as a percentage (e.g., 6) instead of a decimal (0.06) in the formula, which produces a wildly incorrect EAR.
- Using the wrong value of n — for example, entering 12 for a rate that compounds daily (n = 365), understating the true EAR.
- Confusing EAR with APY: while they are the same concept, some financial products quote APY differently (e.g., using a 360-day year), so the numerical result may differ slightly.
Key terms
- What is the effective annual rate (EAR)?
- The actual annual interest rate earned or paid after accounting for compounding within the year. It is always greater than or equal to the nominal rate.
- How does EAR differ from APR?
- APR (Annual Percentage Rate) is a nominal rate that does not account for compounding. EAR (or APY) includes the effect of intra-year compounding and reflects the true annual cost or yield.
- What happens as compounding frequency increases?
- EAR rises as compounding frequency increases, approaching the continuously compounded rate e^r − 1 in the limit.
- When should I use EAR?
- Use EAR to compare financial products with different compounding periods on an equal footing, such as comparing a daily-compounding savings account with a monthly-compounding CD.
Frequently asked questions
- What is the difference between EAR and APR?
- APR is the nominal annual rate without accounting for compounding within the year. EAR converts APR into the true annual rate by incorporating the effect of intra-year compounding, so EAR >= APR.
- Does more frequent compounding always produce a higher EAR?
- Yes, for positive nominal rates. As compounding frequency increases toward continuous compounding, EAR approaches e^r - 1, the theoretical maximum.
- Why does daily compounding vs. monthly compounding matter on a savings account?
- Daily compounding (n=365) applies interest slightly more often than monthly (n=12), resulting in marginally higher EAR and slightly more interest earned over the year.