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What Is the Effective Annual Rate (EAR)?
The effective annual rate calculator answers a deceptively simple question: if a bank quotes you a 6% rate, how much interest will you actually pay or earn in a year? The answer depends entirely on how often the rate compounds. A 6% nominal rate compounded monthly produces an effective annual rate of 6.1678%, because each month a small amount of interest is added to the balance and itself starts earning interest for the rest of the year. The EAR calculator performs that math instantly for any nominal rate and any compounding frequency, so you can compare two financial products on equal terms regardless of how their headline rates are quoted.
EAR is the standard finance-textbook term for what banks call APY on deposits. The two figures are mathematically identical. The asymmetry exists because the Truth in Savings Act requires depositories to label the figure APY, while the academic and professional finance world, including CFA Institute curricula, corporate finance textbooks, and bond pricing literature, uses EAR. According to Investopedia's effective annual interest rate definition, the EAR formula assumes you reinvest all earned interest, which is the default behavior for nearly all deposit accounts and the standard convention for analyzing bond yields.
EAR vs APR: The Critical Difference
Few finance terms are confused as often as APR and EAR. APR (annual percentage rate) is the nominal rate multiplied across the year without accounting for compounding. EAR is the true annual rate after compounding is folded in. The two are equal only when interest compounds annually, every other compounding frequency creates a gap, and the EAR is always the larger figure. Use our APR calculator to see how a lender computes APR from a nominal rate and fees, and then run that same APR through this EAR calculator to see what it truly costs once daily or monthly compounding is taken into account.
On a credit card with an 18% APR compounded daily, the effective annual rate is about 19.72%. The 1.72-percentage-point spread is interest you actually pay but that the APR disclosure understates. The Consumer Financial Protection Bureau requires lenders to disclose APR under Regulation Z, but borrowers who want to know the true cost of a revolving balance need to compute the EAR themselves. Which is exactly what this calculator does. The same logic applies in reverse on a deposit: a bank may quote a nominal rate, but the EAR is the figure that determines how much you actually earn.
The EAR Formula Explained
The effective interest rate calculator uses one formula: EAR = (1 + r/n)^n − 1, where r is the nominal annual rate expressed as a decimal and n is the number of compounding periods per year. For continuous compounding the formula simplifies to EAR = e^r − 1, because the limit of (1 + r/n)^n as n grows without bound is exactly e^r. Let us walk through a concrete example: a 6% nominal rate compounded quarterly means r = 0.06 and n = 4. EAR = (1 + 0.06/4)^4 − 1 = (1.015)^4 − 1 = 1.06136 − 1 = 0.06136 or 6.136%.
The same 6% rate produces 6.0000% EAR if compounded annually, 6.0900% if compounded semi-annually, 6.1364% if compounded quarterly, 6.1678% if compounded monthly, and 6.1831% if compounded daily. The marginal benefit of each step shrinks: moving from annual to quarterly adds 0.136 percentage points of EAR, but moving from monthly to daily adds only 0.015 percentage points. This is why nearly every consumer bank stops at daily compounding. There is no meaningful gain from going further. To see the same compounding dynamic play out over multiple years rather than inside a single year, use our compound interest calculator, which models multi-decade growth on a starting balance.
EAR vs APY: Are They the Same?
EAR and APY are mathematically identical, both use (1 + r/n)^n − 1, and both express the true annual return after compounding. The difference is purely a labeling convention. Banks call it APY because federal Truth in Savings rules require that label on deposit accounts. Academic finance and the bond world call it EAR. International markets sometimes use AER (annual equivalent rate). All four terms refer to the same number. Our annual percentage yield calculator and this effective annual rate calculator return the same result for any given nominal rate and compounding frequency.
Why does the financial industry use two terms for the same concept? Marketing. APY is the figure depositors see on savings account ads because it makes the rate look as high as possible; EAR is the figure used in bond and corporate finance because it standardizes yield comparison across instruments with different coupon frequencies. The CFA Institute's time-value-of-money curriculum uses EAR as the canonical term and walks practitioners through converting nominal coupon rates to effective annual rates as a prerequisite for fixed-income analysis.
Why Compounding Frequency Matters
On a $10,000 balance earning a 6% nominal rate for one year, annual compounding pays $600 of interest, monthly compounding pays $616.78, and daily compounding pays $618.31. The differences look small in absolute dollars on a one-year horizon, but they compound themselves over decades. Over 30 years that same $10,000 grows to $57,435 at 6% compounded annually, but to $60,225 at 6% compounded monthly, a $2,790 difference produced entirely by the compounding frequency. The effective annual rate is the single number that captures this advantage in a way you can compare across products.
Compounding frequency is also the reason credit card debt is so corrosive. A card with an 18% APR compounding daily produces an EAR of about 19.72%, while the same 18% APR compounded monthly would yield 19.56%. The extra 0.16 percentage points may not sound like much, but on a $10,000 balance carried for a decade it costs roughly $640 in additional interest. This is why responsible debt comparison always uses the EAR, not the APR, and why anyone shopping for a high-yield savings account, CD ladder, or money market fund should think in EAR terms too. Browse all our deposit and lending tools in the Quant Calculators Banking category to see the full picture of how EAR shapes both sides of the balance sheet.
Five Practical Tips for Using the EAR Calculator
- Compare every rate quote on an EAR basis. Two loans with the same APR can have different EARs if their compounding schedules differ. The effective annual rate calculator strips that ambiguity away.
- Watch for daily compounding on credit cards. A 22% APR compounded daily produces an EAR of about 24.60%. That extra 2.6 points is the true cost of revolving a balance.
- Use the reverse mode on bond yields. When a bond is quoted as an annual effective yield, the reverse mode of the EAR calculator backs out the equivalent semi-annual nominal coupon, useful for comparing US Treasuries to corporate bonds.
- Net out fees before celebrating a high EAR. A 5.10% EAR savings account with a $5 monthly fee earns substantially less in real terms on a small balance. Always compute net yield, not just EAR.
- Continuous compounding is the ceiling. No consumer product uses it, but it tells you the upper bound of what any nominal rate can become. Daily compounding is within 0.001 percentage points of that ceiling at typical bank rates.