EAR Calculator
Calculate Effective Annual Rate for loans and investments with different compounding frequencies
Calculate Effective Annual Rate
The stated or quoted annual interest rate
Choose compounding method
How often interest compounds per year
EAR Results
Formula used: EAR = (1 + r/m)^m - 1
Calculation: (1 + 0.0000/12)^12 - 1
Compounding: 12 times per year
Future Value Calculation
EAR Analysis
Example Calculation
Monthly Compounding Example
Nominal Rate: 12% annual
Compounding: Monthly (12 times/year)
Periodic Rate: 12% ÷ 12 = 1% per month
Formula: (1 + 0.12/12)^12 - 1
Result
EAR = (1 + 0.01)^12 - 1
EAR = 1.126825 - 1
EAR = 12.6825%
The EAR is higher than the 12% nominal rate due to monthly compounding.
Compounding Frequency Impact
Annual
Lowest EAR, same as nominal
Compounds once per year
Monthly
Common for loans and savings
Moderate compounding effect
Continuous
Maximum possible EAR
Theoretical upper limit
EAR Tips
EAR is always ≥ nominal rate (except when compounding annually)
Higher compounding frequency = higher EAR
Use EAR to compare different investment options
EAR shows the true cost of borrowing or return on investment
Understanding Effective Annual Rate (EAR)
What is EAR?
The Effective Annual Rate (EAR) is the annual rate of interest that is actually earned or paid on an investment, loan or other financial product due to the result of compounding over a given time period. It is also called the effective interest rate, effective rate, or annual equivalent rate.
Why is EAR Important?
- •Provides true comparison between different financial products
- •Accounts for the effect of compounding frequency
- •Required disclosure for many financial products
- •Helps make informed financial decisions
EAR Formulas
Discrete Compounding
EAR = (1 + r/m)^m - 1
- r: Nominal annual interest rate
- m: Number of compounding periods per year
Continuous Compounding
EAR = e^r - 1
- e: Mathematical constant ≈ 2.71828
- r: Nominal annual interest rate
Compounding Frequency Examples
| Frequency | Periods/Year | 12% Nominal → EAR | Difference |
|---|---|---|---|
| Annual | 1 | 12.0000% | - |
| Semi-annual | 2 | 12.3600% | +0.36% |
| Quarterly | 4 | 12.5509% | +0.55% |
| Monthly | 12 | 12.6825% | +0.68% |
| Daily | 365 | 12.7475% | +0.75% |
| Continuous | ∞ | 12.7497% | +0.75% |