EAR Calculator
Calculate Effective Annual Rate (EAR) from APR with different compounding frequencies. Essential for comparing investment returns and loan costs.
Calculate Effective Annual Rate
Results
Effective Annual Rate
0.00%
True annual return
Key Metrics
Nominal Rate (APR):
0.00%
Compounding Frequency:
-
Rate Difference:
0.00%
Compounding Benefit:
$0.00
Investment Growth
$1,000 grows to:
$0.00
$10,000 grows to:
$0.00
Time to double:
0.0 years
Rate Assessment
-
Calculate to see rate assessment
Interpretation
Enter values to see EAR analysis and financial insights.
Compounding Effect Visualization
Understanding Effective Annual Rate (EAR)
The Effective Annual Rate (EAR) represents the actual annual rate of return on an investment or the true cost of a loan, accounting for the effect of compounding.
Key Concepts
- APR vs EAR: APR is the nominal rate; EAR accounts for compounding frequency
- Compounding Effect: More frequent compounding increases the effective rate
- True Comparison: EAR allows accurate comparison between different investment options
- Real Returns: Inflation-adjusted returns show purchasing power changes
EAR Formulas
Standard Formula: EAR = (1 + APR/n)^n - 1
Continuous Compounding: EAR = e^(APR) - 1
From Investment Performance: EAR = (FV/PV)^(1/t) - 1
After-Tax EAR: EAR × (1 - Tax Rate)
Real Return: (1 + EAR) / (1 + Inflation) - 1
Compounding Frequencies
- Annual (n=1): Interest compounded once per year
- Semi-annual (n=2): Compounded twice per year
- Quarterly (n=4): Compounded four times per year
- Monthly (n=12): Most common for loans and savings
- Daily (n=365): High-frequency compounding
- Continuous: Mathematical limit of compounding frequency
Applications and Analysis
Investment Applications
- Portfolio Comparison: Compare returns across different investment vehicles
- Bond Analysis: Evaluate bond yields with different payment frequencies
- Savings Accounts: Compare banks offering different compounding schedules
- Retirement Planning: Calculate true growth rates for long-term planning
Lending Applications
- Credit Cards: Understand true cost of carrying balances
- Mortgages: Compare loans with different compounding terms
- Personal Loans: Evaluate total borrowing costs
- Business Financing: Assess financing options accurately
Factors Affecting EAR
- Compounding Frequency: Higher frequency increases EAR
- Nominal Rate: Base rate before compounding effects
- Time Period: Longer periods amplify compounding benefits
- Tax Implications: Taxes reduce effective returns
- Inflation: Erodes real purchasing power of returns
Decision Making Guidelines
- Investment Selection: Choose options with highest EAR for similar risk
- Loan Comparison: Select loans with lowest EAR for same terms
- Tax Planning: Consider after-tax EAR for investment decisions
- Inflation Protection: Ensure real returns meet financial goals
- Risk Assessment: Higher EAR may indicate higher risk