Effective Annual Rate (EAR) Calculator
Convert a nominal annual rate into the effective annual rate for any compounding frequency, including continuous compounding.
Result
- Nominal rate (APR)6.000%
- Compounding12×/year
- Effective annual rate6.1678%
- Compounding premium over nominal0.1678%
- Annually6.0000%
- Semiannually6.0900%
- Quarterly6.1364%
- Monthly6.1678%
- Daily6.1831%
- Continuous (e^r − 1)6.1837%
Step-by-step
- EAR = (1 + 0.06/12)^12 − 1 = 6.1678%.
- That is 0.1678% more than the nominal rate, due to compounding within the year.
- More frequent compounding raises the EAR, approaching the continuous limit.
How to use this calculator
- Enter the nominal annual rate (the stated APR).
- Choose how often it compounds, or select continuous.
- Read the effective annual rate (EAR/APY).
- Use the side-by-side table to compare frequencies.
About this calculator
The nominal annual rate (APR) on a loan or savings account does not, by itself, tell you how much interest actually accrues in a year — that depends on how often it compounds. The effective annual rate (EAR), also called the annual percentage yield (APY) for deposits, captures the real yearly cost or return by accounting for compounding within the year. This calculator converts a nominal rate to its EAR for any frequency — annual, semiannual, quarterly, monthly, weekly, daily, or continuous — using EAR = (1 + nominal/m)^m − 1, with the continuous case given by e raised to the nominal rate, minus one. The more frequently interest compounds, the higher the EAR climbs above the nominal rate, approaching the continuous limit. The tool also shows the EAR at several common frequencies side by side, so you can compare offers on an apples-to-apples basis — always EAR to EAR, never APR to APY.
How it works — the formula
EAR = (1 + nominal/m)^m − 1 (m compounds per year)
Continuous: EAR = e^nominal − 1Compounding the nominal rate m times a year and annualizing gives the effective rate; infinite compounding yields the continuous formula.
Worked examples
- Inputs:
- nominal=6, freq=12
- Output:
- EAR 6.1678%
- Inputs:
- nominal=6, freq=365
- Output:
- EAR 6.1831%
- Inputs:
- nominal=6, freq=0
- Output:
- EAR 6.1837%
Limitations
- Assumes a constant nominal rate.
- Ignores fees that change the true cost (APR with fees differs).
- Continuous compounding is a theoretical limit.
Rate conversion; compare like-for-like (EAR to EAR).