Effective Interest Rate Calculator
The Rate Behind the Rate
A "nominal" interest rate is the stated annual figure, but it doesn't account for how often that interest compounds. The Effective Annual Rate (EAR) does — it converts a nominal rate and its compounding schedule into the real annual rate you'd actually experience, which is what should be used to compare two loans, bonds, or accounts that compound differently.
The Formula
Continuous compounding: EAR = ei − 1
i is the nominal annual rate (as a decimal) and n is the number of compounding periods per year. Continuous compounding represents the mathematical limit as compounding frequency approaches infinity, using Euler's number e.
Why the Distinction Matters
- Loan comparisons — two loans quoting the same nominal rate can carry different true costs if they compound on different schedules.
- Investment products — bonds, CDs, and structured products sometimes quote nominal rates specifically because it makes the headline number look lower than the effective cost or yield.
- Regulatory disclosure — EAR-style disclosure exists precisely because nominal rates alone can be misleading without knowing the compounding frequency.
8% Nominal Rate at Different Compounding Frequencies
| Compounding | Effective Annual Rate |
|---|---|
| Annually | 8.0000% |
| Semi-Annually | 8.1600% |
| Quarterly | 8.2432% |
| Monthly | 8.3000% |
| Daily | 8.3278% |
| Continuous | 8.3287% |
Continuous compounding is the theoretical ceiling — note how close daily compounding already gets to it.
How to Use This Calculator
- Enter the Nominal Annual Interest Rate as a percentage.
- Select the compounding frequency — annually, semiannually, quarterly, monthly, daily, or continuously.
- Select Calculate to see the Effective Annual Rate.
Related Calculations
To see this same concept applied to a savings account specifically, use the APY Calculator, or account for loan fees with the APR Calculator.