Effective Annual Rate (EAR) Calculator
Calculate the Effective Annual Rate (EAR) from a nominal interest rate.
Compare loans or investments that compound at different frequencies on equal terms.
What Is the Effective Annual Rate (EAR)?
The Effective Annual Rate (EAR) — also called the Annual Percentage Yield (APY) — is the actual annual rate of return on an investment or the actual annual cost of a loan, after accounting for compounding within the year. It allows you to compare financial products that compound at different frequencies on equal footing.
The EAR Formula
EAR = (1 + r/n)^n − 1
Where:
- r = Nominal annual interest rate (as a decimal)
- n = Number of compounding periods per year
For continuous compounding:
EAR = e^r − 1
Where e ≈ 2.71828 (Euler’s number)
Nominal vs. Effective Rate
The nominal rate (APR — Annual Percentage Rate) is the stated rate before compounding. The effective rate (EAR / APY) is what you actually earn or pay after compounding.
The more frequently interest compounds, the higher the EAR relative to the nominal rate.
A Practical Comparison
A 12% nominal rate compounded at different frequencies:
| Compounding | Periods/Year | Effective Annual Rate |
|---|---|---|
| Annually | 1 | 12.000% |
| Semi-annually | 2 | 12.360% |
| Quarterly | 4 | 12.551% |
| Monthly | 12 | 12.683% |
| Daily | 365 | 12.747% |
| Continuously | — | 12.750% |
For a $10,000 loan at 12% nominal for one year, the difference between annual and daily compounding is $74.70 — significant at scale.
Why Banks and Lenders Use These Rates Strategically
Lenders often advertise the lower nominal APR; savings products advertise the higher APY. Knowing both lets you make informed comparisons. Always ask: “Is this rate APR or APY?”
Credit Cards: The Hidden Cost
Credit cards typically charge 20%–29% APR but compound daily. A 24% APR compounded daily has an EAR of about 27.11% — meaning your effective annual cost is notably higher than the advertised rate.
Mortgages
In the United States, mortgages are quoted as APR (nominal, compounded monthly). The effective rate is slightly higher. In Canada, mortgages are quoted as nominal rates compounded semi-annually but paid monthly — requiring a conversion to find the true effective rate.