Effective Annual Rate Calculator

The effective annual rate shows what a nominal rate really earns once compounding is included: \(\text{EAR} = \left(1 + \frac{r}{n}\right)^{n} – 1\). A 12% rate compounded monthly is (1.01)¹² − 1 = 12.68% a year.

How to use the effective annual rate calculator

1. Choose the direction: APR to EAR, or EAR back to APR.
2. Enter the rate and how often interest is compounded.
3. Press Calculate to see the rate and a table for every compounding frequency.

Formulas

• \(\text{EAR} = \left(1 + \frac{r}{n}\right)^{n} – 1\)
• Continuous: \(\text{EAR} = e^{r} – 1\)
• Back to APR: \(r = n\left[(1 + \text{EAR})^{1/n} – 1\right]\), or \(\ln(1 + \text{EAR})\) for continuous

EAR vs APR vs APY

APR is the nominal yearly rate before compounding. The EAR includes compounding; for savings accounts in the U.S. the same idea is called the annual percentage yield (APY). The more often interest compounds, the higher the EAR, but the gains get small: 12% gives 12.36% semiannually, 12.68% monthly, 12.75% daily and 12.75% continuously.

Worked example

A card charges 24% APR compounded monthly: \(\left(1 + \frac{0.24}{12}\right)^{12} – 1 = 1.02^{12} – 1 \approx 26.82\%\). Carrying a $1,000 balance for a year without payments costs about $268, not $240.

Effective annual rate practice quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

What is the effective annual rate?

The yearly interest rate after accounting for compounding. It lets you compare rates with different compounding periods.

How is EAR different from APR?

APR is the stated yearly rate without compounding. EAR is what you actually earn or pay in a year when interest compounds.

Is EAR the same as APY?

Yes, in practice. APY is the term U.S. banks use for the effective yearly rate on deposits.

What does continuous compounding mean?

Interest is added constantly; the EAR is e^r − 1, the upper limit for a given APR.

Can I convert EAR back to APR?

Yes. Choose EAR → nominal rate and pick the compounding.

Sources

• CFPB: What is the difference between APR and APY?
• Corporate Finance Institute: Effective Annual Interest Rate

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