EAR Calculator
Basic EAR using only Nominal Rate & Compounding
Effective Annual Rate (EAR)
0.00%
Related Calculators
EAR Calculator – Full Guide
Table of Contents
Introduction
The EAR calculator helps you understand how your interest grows when compounding is applied more than once per year. It converts a nominal rate into a true annual return, showing the actual earning potential.
Interest added monthly or daily makes money grow faster. Using the calculator gives better transparency in financial decisions such as investments, loans, and credit cards.
With EAR, you always know the real cost or real return behind the number advertised by financial institutions.
What is Effective Annual Rate?
The effective annual rate expresses how interest truly accumulates over a full year when compounding happens periodically. It tells how much interest is earned from your principal after compounding adjustments.
Unlike nominal rates that may seem attractive but hide compounding effects, EAR offers clear insight. If two banks offer different compounding frequencies, EAR helps you pick the stronger return.
EAR is always equal to or greater than the nominal rate whenever compounding is more frequent than annually.
Why EAR Matters / Benefits
- Shows the real return on investment
- Helps compare different financial products accurately
- Reveals the hidden impact of compounding
- Used widely in bank savings and loan decisions
- Helps avoid misleading nominal interest rates
When comparing two rates with different compounding intervals, EAR always points to the truly profitable one.
Inputs Explained
To compute the result using this tool, you only need two essential inputs:
- Nominal interest rate: The stated yearly rate without compounding effects.
- Compounding frequency: How many times interest is added in a year.
More compounding cycles increase the effective return. Selecting the right compounding frequency is crucial.
How the Calculation Works (Step-by-Step)
The compound interest effect amplifies earnings because each compounding cycle adds new interest based on previously earned interest.
- Convert nominal rate to decimal
- Divide by compounding periods per year
- Add 1 to the result
- Raise to the power of number of compounding periods
- Subtract 1 to get the true effective rate
These steps allow precise financial evaluation across multiple offers.
Examples
Example 1: Monthly Compounding
Nominal = 10%, Compounding = 12 times yearly
EAR = (1 + 0.10/12)^12 - 1 = approx 10.47%
More frequent compounding slightly increases actual returns.
Example 2: Quarterly Compounding
Nominal = 8%, Compounding = 4 times yearly
EAR = approx 8.24%
Less frequent compounding yields a slightly lower return.
Example 3: Daily Compounding
Nominal = 6%, Compounding = 365 times yearly
EAR = approx 6.18%
Daily compounding boosts returns further.
Example 4: No Compounding Benefit (Yearly)
Nominal = 7%, Compounding = once yearly
EAR = 7%
No compounding effect when interest applies only once per year.
Example 5: Comparing Two Offers
Bank A: 9% quarterly vs Bank B: 9% monthly
Bank B will offer higher true returns via compounding advantage.
Formulas
EAR = (1 + r/n)^n − 1
r = nominal rate in decimal form n = number of compounding periods per year
EAR difference = EAR offer A − EAR offer B
EAR Table for Different Compounding Frequencies
The following example assumes a 10% nominal rate:
| Frequency | n | EAR |
|---|---|---|
| Yearly | 1 | 10.00% |
| Semi-Annual | 2 | 10.25% |
| Quarterly | 4 | 10.38% |
| Monthly | 12 | 10.47% |
| Weekly | 52 | 10.51% |
| Daily | 365 | 10.52% |
| Continuous | ∞ | 10.52%+ |
More cycles amplify total growth without changing the nominal rate.
Comparison of Nominal vs EAR
| Nominal | Compounding | EAR |
|---|---|---|
| 5% | Yearly | 5.00% |
| 5% | Monthly | 5.12% |
| 8% | Quarterly | 8.24% |
| 9% | Monthly | 9.38% |
| 6% | Daily | 6.18% |
| 10% | Weekly | 10.47% |
| 12% | Monthly | 12.68% |
Nominal values alone never show the correct return.
Daily Compounding Impact
| $ Amount Invested | Nominal Rate | EAR | Gain |
|---|---|---|---|
| $1000 | 6% | 6.18% | $61.80 |
| $2000 | 7% | 7.25% | $145.00 |
| $5000 | 8% | 8.33% | $416.50 |
| $10000 | 9% | 9.38% | $938.00 |
| $25000 | 10% | 10.52% | $2630.00 |
| $30000 | 11% | 11.62% | $3486.00 |
| $50000 | 12% | 12.68% | $6340.00 |
Daily compounding consistently outperforms yearly calculations.
Tips & Best Practices
- Compare savings and loan offers using EAR only
- Always ask financial institutions for compounding frequency
- Be cautious when nominal rate appears high but compounding is low
- Greater frequency leads to stronger annual growth
- Check EAR for fairness when borrowing
Small compounding differences add up over longer investment periods.
Limitations
- Does not include taxes or inflation
- Assumes interest rate remains constant
- Ignores market volatility
Real-world outcomes vary depending on fees, economic conditions, and personal behavior.
Conclusion
The EAR calculator has become an indispensable tool for smarter decision-making in modern financial planning. It reveals the real growth impact of compounding and helps select the most rewarding option.
Whether comparing savings accounts, loans, or investment products, always rely oneffective annual rate to judge performance correctly.
Understanding compounding gives you the ultimate advantage in long-term wealth creation.