A rate’s headline number does not tell you how much interest you will actually earn or pay. That depends on how often interest is compounded — added to the balance so it starts earning interest itself. The effective annual rate (EAR), called the annual percentage yield (APY) on deposit accounts, folds compounding into one number so you can compare a 4.9% rate compounded daily with a 5% rate compounded annually on equal terms.
How to use the effective annual rate calculator
- Enter the nominal annual rate — the APR or stated rate.
- Choose the compounding frequency, from annually to daily or continuously.
- Optionally enter an amount to see the interest it would earn or cost in one year.
- Read the EAR, then compare all compounding frequencies and a range of common rates in the tables.
EAR formula
r is the nominal annual rate as a decimal and m is the number of compounding periods per year. The term r/m is the periodic rate charged or paid each period.
Worked example
A savings account pays 5% compounded monthly:
Periodic rate: 0.05 ÷ 12 = 0.00416667
EAR = (1.00416667)12 − 1 = 0.0511619 = 5.1162%
On $10,000 that is $511.62 of interest in a year, instead of $500 with no compounding.
5% at every compounding frequency
| Compounding | EAR (APY) | Interest on $10,000 |
|---|---|---|
| Annually | 5.0000% | $500.00 |
| Semi-annually | 5.0625% | $506.25 |
| Quarterly | 5.0945% | $509.45 |
| Monthly | 5.1162% | $511.62 |
| Daily | 5.1267% | $512.67 |
| Continuously | 5.1271% | $512.71 |
Each step up in frequency adds less than the one before, and continuous compounding is the ceiling. Frequency matters more at higher rates: 18% compounded monthly is 19.56% effective, and 25% becomes 28.07%.
Where EAR and APY show up
Savings accounts and CDs
The Truth in Savings Act and its Regulation DD require banks to disclose APY so savers can compare accounts that compound differently. When two banks quote APYs, the higher APY pays more, regardless of how each compounds.
Loans and credit cards
Loans are disclosed by APR, which does not include compounding. A credit card at 24% APR charges a periodic rate each billing cycle, so its effective cost if a balance is carried all year is about 26.8% with monthly compounding. Converting APR to EAR shows the true annual cost.
Comparing investments
When returns are reported quarterly or monthly, annualize them with the same formula before comparing them with annual figures.
Related conversions
Going the other direction — from an APY back to a nominal rate — uses the nominal interest rate calculator. To restate a rate from one compounding frequency to another, use the equivalent interest rate calculator, and for the effective rate over a period shorter or longer than a year, the effective interest rate calculator.
Results are mathematical conversions. Banks' disclosed APYs follow Regulation DD and may differ slightly for accounts with fees, tiered rates or terms shorter than a year.
Frequently asked questions
What is the effective annual rate?
The effective annual rate (EAR) is the interest actually earned or paid in one year once compounding is included. For savings it is usually called the annual percentage yield (APY). A 5% rate compounded monthly has an EAR of 5.1162%.
What is the formula for EAR?
EAR = (1 + r/m)^m − 1, where r is the nominal annual rate as a decimal and m is the number of compounding periods per year. For continuous compounding, EAR = e^r − 1.
What is the difference between APR and APY?
APR is a nominal rate: the periodic rate times the number of periods, without compounding. APY is the effective rate that includes compounding. Lenders disclose APR on loans under the Truth in Lending Act, while banks disclose APY on deposits under the Truth in Savings Act.
Does daily compounding make a big difference?
Not much compared with monthly. At 5%, monthly compounding gives 5.1162% and daily gives 5.1267%, a difference of about $1 a year on $10,000. The gap grows at higher rates: 18% compounded monthly is 19.56% effective.