EAR Calculator (Effective Annual Rate)

What is the effective annual rate?

The effective annual rate is the annual interest rate after compounding. Lenders and banks usually quote a nominal (stated) rate, then add interest several times a year. Each time interest is added, the next period's interest is charged on a slightly bigger balance, so the true yearly rate ends up higher than the stated one.

That is why two products with similar headline rates can cost or earn noticeably different amounts. EAR – also called the effective annual interest rate, the annual equivalent rate (AER) in the UK, or APY on US savings accounts – puts every offer on the same once-a-year basis so you can compare them fairly.

EAR formula

• EAR = (1 + r/m)^m − 1
• r = nominal annual rate as a decimal (8% = 0.08)
• m = number of compounding periods per year
• r/m = the periodic rate charged each period
• Continuous compounding: EAR = e^r − 1, where e ≈ 2.71828

How to calculate effective annual rate step by step

1. Convert the nominal rate to a decimal: 8% → 0.08.
2. Divide by the number of periods: 0.08 ÷ 12 = 0.006667 (0.667% a month).
3. Add 1 and raise to the power of m: 1.006667^12 = 1.083000.
4. Subtract 1 and convert back to a percentage: EAR = 8.300%.

With continuous compounding the same 8% becomes e^0.08 − 1 = 8.329%. That is the upper limit: compounding more often than daily adds almost nothing.

How compounding frequency changes EAR

The table shows a 6% nominal rate under each common schedule. The jump from annual to monthly is large; the jump from monthly to daily is small.

EAR vs APR vs APY

APR and EAR answer different questions. APR is a disclosure figure that can include fees, while EAR isolates the effect of compounding. For a credit card, the APR divided by 365 is the daily periodic rate; EAR shows what that daily rate adds up to if a balance is carried for a full year.

Worked examples with real numbers

Comparing two mortgage quotes

Lender A quotes 6.5% compounded monthly and Lender B quotes 6.4% compounded daily. A's EAR is 6.697% and B's is 6.609%, so B is cheaper despite compounding more often – the lower stated rate wins here. Frequency only flips the result when the stated rates are very close or the frequencies are very different, which is why checking the EAR beats guessing.

The credit-card balance

A card with a 24% APR compounded daily has a daily rate of 0.0658%. Carried for a year, that compounds to an EAR of 27.115%. On a $3,000 balance with no payments, the interest is about $813 rather than the $720 the APR suggests.

Two savings accounts at 4%

Both accounts pay 4% nominal. Monthly compounding gives an EAR of 4.074% and daily compounding 4.081%. On $10,000 over a year that is $407.42 versus $408.08 – only 67 cents apart, so a higher stated rate matters far more than a more frequent schedule.

Converting EAR back to a nominal rate

Sometimes you know the effective rate you want and need the nominal rate to quote. Rearranging the formula gives r = m × [(1 + EAR)^(1/m) − 1]. For a 10% EAR with monthly compounding: 12 × (1.10^(1/12) − 1) = 9.569%. The calculator's reverse mode does this for any frequency.

Limits of EAR

• EAR ignores fees, so for loans compare it alongside the APR and total cost.
• It assumes the rate stays fixed for the whole year; variable rates change the answer.
• For a balance you pay off each month in full, a card's EAR does not apply – no interest is charged.
• Rates and how lenders disclose them vary by country; check the official disclosure for your loan.

Sources

1. CFPB – What is the difference between an APR and an interest rate? — consumerfinance.gov
2. Investor.gov – Compound interest calculator — investor.gov
3. Corporate Finance Institute – Effective annual rate — corporatefinanceinstitute.com