Effective annual rate calculator
The effective annual rate shows what a nominal rate really earns or costs in a year once interest is compounded. Choose how often it compounds, from yearly to daily or continuously, and enter the nominal rate to get the EAR. You can also work backwards from an EAR to the nominal rate.
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How to use it
- Choose the direction: nominal rate to EAR, or EAR to nominal rate.
- Enter the rate in percent and pick the compounding frequency.
- Read the result and what 1,000 would grow to in a year.
How it works
- Nominal to EAR: EAR = (1 + r ÷ m)^m − 1, or e^r − 1 when compounding continuously.
- EAR to nominal: r = m × ((1 + EAR)^(1 ÷ m) − 1), or ln(1 + EAR) for continuous.
- Rate per period = nominal rate ÷ m.
Worked example
A nominal 10% compounded semiannually pays 5% every half year: 1.05 × 1.05 = 1.1025, so the EAR is 10.25%, and 1,000 grows to 1,102.50 in a year.
Tips
- Compare offers by EAR, not by nominal rates with different compounding.
- Weekly and daily use 52 and 365 periods a year here; some banks use 360.
- Fees are not part of EAR.
Frequently asked questions
What is the effective annual rate?
It is the yearly rate that gives the same result as the nominal rate compounded several times a year. A nominal 12% compounded monthly is 1% a month, which grows 1 to 1.01^12 = 1.126825, an EAR of 12.6825%.
What is the formula?
EAR = (1 + r ÷ m)^m − 1, where r is the nominal annual rate as a fraction and m the number of compounding periods a year. For continuous compounding it is e^r − 1.
Is EAR the same as APY?
They describe the same idea: the annual rate including compounding. APY is the usual name for savings accounts. APR on a loan is normally a different calculation, which may include fees.
Why does more frequent compounding raise the EAR?
Interest earned early starts earning interest itself sooner. A nominal 10% gives 10.25% compounded semiannually, 10.3813% quarterly and 10.5171% continuously. The gains from compounding more often get smaller each time.
How do I find the nominal rate from the EAR?
Use nominal = m × ((1 + EAR)^(1 ÷ m) − 1). Choose the mode EAR to nominal rate, enter the EAR and the compounding frequency.