Effective Annual Rate
Effective annual rate (EAR) from a nominal rate and compounding.
Effective annual rate
12.6825%
nominal 12%
Nominal rate
12%
Extra vs nominal
0.6825%
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How the Effective Annual Rate works
The Effective Annual Rate (EAR) calculator converts a nominal interest rate into its true annual equivalent by accounting for how often interest compounds throughout the year. It's essential for borrowers comparing loan offers, investors evaluating savings accounts or CDs, and anyone who wants to see past the headline rate to the real cost or return.
At its core, this calculator answers a deceptively simple question: what is the actual interest you earn or pay over a full year when compounding is applied? A nominal rate — also called the stated or annual percentage rate (APR) — tells you the base rate without reflecting how frequently interest is added to your balance. The EAR, sometimes called the Annual Percentage Yield (APY) in a savings context, folds in the compounding schedule so you can make true apples-to-apples comparisons between financial products that use different compounding frequencies.
The mathematics hinge on compounding frequency. When interest is compounded monthly rather than annually, each month's earned interest itself begins earning interest for the remaining months of the year. The more frequently compounding occurs — monthly, daily, or even continuously — the larger the gap between the nominal rate and the EAR. For example, a 12% nominal rate compounded monthly yields an EAR of approximately 12.68%, while the same nominal rate compounded daily yields roughly 12.75%. This difference may seem small on a single-year deposit, but on a mortgage balance or long-term investment it can represent thousands of dollars.
To use the calculator, simply enter your nominal annual interest rate and select the compounding frequency — options typically include annually, semi-annually, quarterly, monthly, daily, or continuously. The tool instantly returns the EAR, giving you the single standardized number needed for comparison. A common mistake is confusing APR with APY: in the US, lenders are required to disclose APR (which may still exclude certain fees), while deposit institutions typically advertise APY, which is already the EAR. Always verify which figure you're looking at before plugging numbers in.
Strategically, savvy borrowers use the EAR to identify which loan is truly cheaper when lenders quote different compounding schedules, and investors use it to confirm which savings vehicle actually pays more. If you're considering continuous compounding — common in theoretical finance and some foreign instruments — the EAR formula takes a special exponential form. Understanding EAR also helps when evaluating credit card debt, which typically compounds daily, making the true annual cost noticeably higher than the stated purchase APR.
Formula
EAR = (1 + r/n)ⁿ − 1
Pro tips
- Always compare financial products using EAR or APY, not the nominal rate — two accounts advertising the same nominal rate can yield meaningfully different returns if their compounding schedules differ.
- When evaluating credit cards, remember that most compound interest daily. Enter your card's purchase APR with daily (365) compounding into the EAR calculator to see the true annual cost before carrying a balance.
- If a bank advertises APY on a savings account, that number is already the EAR — do not run it through the calculator again. Only convert nominal (APR-style) rates to EAR.
- For mortgage or loan comparisons, request the exact compounding frequency from each lender, then use the EAR to identify the genuinely cheaper option rather than relying on the quoted APR alone.
- When modeling investment growth or debt payoff, use the periodic rate derived from EAR (EAR divided by periods per year) in your spreadsheet rather than the nominal rate — this keeps your projections accurate.
Key terms
- Nominal Rate
- — The stated annual interest rate before the effects of compounding are factored in, often called APR in lending contexts.
- Effective Annual Rate (EAR)
- — The true annual interest rate that accounts for compounding within the year, representing the real cost of borrowing or return on investment.
- APY (Annual Percentage Yield)
- — The US regulatory term for EAR as applied to deposit accounts; it reflects the actual interest earned on a deposit in one year including compounding.
- Compounding Frequency
- — How often interest is calculated and added to the principal balance — annually, quarterly, monthly, daily, or continuously — directly determining how much EAR exceeds the nominal rate.
- Continuous Compounding
- — A theoretical compounding scenario where interest is calculated and added to the balance at every infinitesimal moment, yielding the maximum possible EAR for a given nominal rate.
- APR (Annual Percentage Rate)
- — A US-regulated disclosure figure for loans that reflects the nominal interest rate and certain fees but does not account for intra-year compounding.