📊 Effective Annual Rate Calculator
Calculate the Effective Annual Rate (EAR) from a nominal interest rate with different compounding frequencies. Compare annual, semi-annual, quarterly, monthly, daily, and continuous compounding to find the true cost or return of your investment or loan.
What Is the Effective Annual Rate (EAR)?
The Effective Annual Rate (EAR) — also known as Annual Percentage Yield (APY) — is the actual annual rate of return or interest earned on an investment or loan, taking into account the effect of compounding.
Unlike the nominal rate (stated rate), EAR reflects how often interest is compounded within the year. The more frequently interest is compounded, the higher the effective rate will be relative to the nominal rate.
How Does the Effective Annual Rate Calculator Work?
The calculator uses the standard EAR formula:
Where:
- r = Nominal interest rate (as a decimal)
- n = Number of compounding periods per year
For continuous compounding, the formula is:
The calculator also generates a complete comparison table showing the EAR for all common compounding frequencies, helping you see the impact of compounding frequency on your returns or costs.
Why Use This Effective Annual Rate Calculator?
- True Cost Comparison: Compare loans and investments on an apples-to-apples basis.
- All Frequencies: Supports annual, semi-annual, quarterly, monthly, bi-weekly, weekly, daily, and continuous compounding.
- Full Comparison: See the EAR for every compounding frequency in one table.
- Visual Chart: Instantly see how EAR increases with more frequent compounding.
- Free & Private: No registration, no data storage — all calculations run in your browser.
❓ Effective Annual Rate Calculator FAQ
What is the difference between nominal rate and effective annual rate?
The nominal rate is the stated annual interest rate without accounting for compounding. The Effective Annual Rate (EAR) or APY reflects the actual annual return or cost after compounding. EAR is always equal to or higher than the nominal rate when compounding occurs more than once per year.
What is the formula for the Effective Annual Rate?
EAR = (1 + r/n)n − 1 where r is the nominal rate and n is the number of compounding periods per year. For continuous compounding, EAR = er − 1.
How does compounding frequency affect EAR?
More frequent compounding leads to a higher EAR because interest is calculated and added to the principal more often, allowing interest to earn interest. For example, at 8% nominal, monthly compounding gives ~8.30% EAR, while daily compounding gives ~8.33%.
What is continuous compounding?
Continuous compounding assumes interest is compounded an infinite number of times per year. The formula is EAR = er − 1. It represents the theoretical maximum effective rate for a given nominal rate.
Why is EAR important for loans?
Lenders often advertise the nominal rate, but the EAR shows the true cost of borrowing. Comparing the EAR of different loans helps you choose the cheapest option. The Truth in Lending Act requires lenders to disclose the APR (which is similar to EAR) in the U.S.
Why is EAR important for investments?
Banks and investment accounts often advertise the nominal rate, but the EAR (or APY) shows your actual return. Comparing the EAR of different investment products helps you maximize your returns.
What is the difference between EAR and APR?
EAR (Effective Annual Rate) and APR (Annual Percentage Rate) are similar but have subtle differences. EAR reflects the true cost of borrowing or return on investment after compounding. APR often includes fees and costs in addition to interest, but may not account for the full effect of compounding depending on the calculation method.
How accurate is this calculator?
This calculator provides accurate results based on standard financial formulas. The EAR is calculated precisely using the correct mathematical formulas. Use it as a reliable tool for comparing financial products.
Is this calculator free to use?
Yes, this calculator is completely free to use. No registration or personal data storage is required. All calculations are performed in your browser.
How do I compare loans with different compounding frequencies?
Use this calculator to convert each loan's nominal rate to its EAR. The loan with the lowest EAR has the lowest true cost, regardless of how often interest is compounded.