EAR Calculator
Calculate the Effective Annual Rate (EAR) from nominal interest rates. EAR shows the true annual rate when compounding is considered, helping you compare different financial products accurately.
EAR Results
Rate Comparison
Add comparisons above to see results
Common EAR Examples
Credit Cards: 15-25% APR ? 16-27% EAR
Personal Loans: 10-20% APR ? 10-22% EAR
Savings Accounts: 4-5% APY ? 4-5% EAR
Tip: Always compare EAR for accurate comparisons
Understanding Effective Annual Rate (EAR)
Effective Annual Rate (EAR) represents the true annual interest rate when compounding is taken into account. It shows what you would actually earn or pay over a year, making it easier to compare different financial products.
EAR Formula
The formula for calculating EAR is:
EAR = (1 + r/n)^n - 1
Where: r = nominal annual rate, n = number of compounding periods per year
EAR vs. Nominal Rate
| Aspect | Nominal Rate | Effective Annual Rate (EAR) |
|---|---|---|
| What it shows | Stated annual rate | True annual rate with compounding |
| Compounding effect | Ignores compounding | Includes compounding effect |
| Comparison tool | Limited usefulness | Best for accurate comparisons |
| Always true | EAR = Nominal Rate | When compounding occurs |
Impact of Compounding Frequency
More frequent compounding results in higher EAR. The difference becomes more significant with higher nominal rates.
| Compounding | 10% Nominal Rate | 20% Nominal Rate |
|---|---|---|
| Annually | 10.00% | 20.00% |
| Quarterly | 10.38% | 21.55% |
| Monthly | 10.47% | 21.94% |
| Daily | 10.52% | 22.13% |
EAR in Different Contexts
- Savings & Investments: Shows true return on deposits and investments
- Credit Cards: Reveals true cost of borrowing (APR to EAR)
- Loans: Helps compare different loan terms and rates
- Mortgages: Compares different mortgage products
- Business Finance: Evaluates cost of capital and investment returns
Regulatory Requirements
Many countries require financial institutions to disclose EAR alongside nominal rates to ensure consumers can make informed decisions.
- Truth in Lending Act (US): Requires EAR disclosure for consumer loans
- Consumer Credit Directive (EU): Mandates EAR disclosure
- Banking Regulations: EAR required for deposit and loan products
- Investment Products: Mutual funds and ETFs must show EAR
Common EAR Calculations
Credit Card Example
Credit card with 18% APR compounded monthly:
- Nominal Rate: 18%
- EAR: (1 + 0.18/12)^12 - 1 = 19.56%
- True annual cost is 19.56%, not 18%
Savings Account Example
Savings account with 4.5% APY compounded quarterly:
- Nominal Rate: 4.5%
- EAR: (1 + 0.045/4)^4 - 1 = 4.60%
- You earn 4.60% on your money annually
When EAR Matters Most
- High Nominal Rates: Larger difference between nominal and EAR
- Frequent Compounding: More compounding periods increase EAR
- Long Time Horizons: Compounding effect grows over time
- Multiple Options: Comparing different financial products
- Cost of Borrowing: Understanding true cost of credit
Tip: Always calculate EAR when comparing different financial products. The nominal rate alone can be misleading, especially for products with different compounding frequencies. EAR gives you the true annual rate, helping you make better financial decisions.