Effective Interest Rate Calculator
Calculate the true annual interest rate when compounding is taken into account
| Compounding | Periods/Year | Effective Rate |
|---|---|---|
| Annually | 1 | - |
| Semi-Annually | 2 | - |
| Quarterly | 4 | - |
| Monthly | 12 | - |
| Daily | 365 | - |
| Continuous | ∞ | - |
The Effective Annual Rate (EAR) is the actual interest rate that an investor earns or pays in a year after accounting for compounding. It differs from the nominal rate because it considers how often compounding occurs.
• Comparing loans with different compounding periods
• Evaluating investment returns
• Understanding credit card APRs
• Calculating mortgage interest
• More frequent compounding = higher EAR
• Continuous compounding gives the maximum EAR
• Always compare EAR when evaluating options
• Nominal rates can be misleading
An Effective Interest Rate (EIR) Calculator helps you determine the true cost of borrowing or the real return on investments by accounting for compounding periods. Unlike nominal rates, EIR reveals what you actually pay or earn annually.
How the Effective Interest Rate Calculator Works
Formula
Where:
r = Nominal annual interest rate (decimal)
n = Number of compounding periods per year
Example Calculation
| Input | Value |
|---|---|
| Nominal Rate (APR) | 6.00% |
| Compounding Frequency | Monthly (n=12) |
| Effective Rate (EIR) | 6.17% |
Key Insight:
The 6% nominal rate becomes 6.17% EIR due to monthly compounding.
Key Inputs Required
Nominal Interest Rate (APR)
Stated annual rate before compounding
Compounding Frequency
Daily (365), Monthly (12), Quarterly (4), etc.
Optional: Fees or additional costs (for loans)
Why EIR Matters More Than Nominal Rates
✅ Loan Comparisons - Reveals the true cost of credit cards, mortgages, and personal loans
✅ Investment Decisions - Shows real returns on savings accounts, CDs, and bonds
✅ Regulatory Compliance - Required disclosure for financial products in many countries
Common Applications
1. Loans (Borrowing Cost)
| Loan Type | Nominal Rate | Compounding | EIR |
|---|---|---|---|
| Credit Card | 18% | Daily | 19.56% |
| Personal Loan | 12% | Monthly | 12.68% |
| Mortgage | 5% | Semi-annual | 5.06% |
2. Investments (Real Returns)
| Account | Nominal Rate | Compounding | EIR |
|---|---|---|---|
| Savings | 4.5% | Daily | 4.60% |
| CD | 5% | Quarterly | 5.09% |
| Money Market | 4.25% | Monthly | 4.33% |
EIR vs. Related Rates
| Rate Type | Includes Compounding? | Common Uses |
|---|---|---|
| Nominal (APR) | No | Advertising rates |
| Effective (EIR) | Yes | True cost/return analysis |
| Annual Percentage Yield (APY) | Yes | Banking products |
Step-by-Step Calculation
Convert nominal rate to decimal (6% → 0.06)
Divide by compounding periods (0.06 ÷ 12 = 0.005)
Add 1 (1 + 0.005 = 1.005)
Raise to power of periods (1.005¹² ≈ 1.0617)
Subtract 1 (1.0617 - 1 = 0.0617 → 6.17%)
Special Cases
Continuous Compounding
(Where *e* ≈ 2.71828)
Example: 5% nominal → 5.13% EIR
Including Fees
For loans with origination fees:
Add fees to total interest
Recalculate EIR on adjusted amount
Pro Tips
✔ Compare All Loans Using EIR - A 5% loan compounding daily costs more than 5.5% annually
✔ Seek Daily Compounding for Savings - Maximizes returns
✔ Watch for "Teaser Rates" - Some loans show low nominal rates but high EIRs
Real-World Impact
$10,000 Loan at 12% Nominal Rate:
Annual compounding: 12.00% EIR ($1,200 interest)
Monthly compounding: 12.68% EIR ($1,268 interest)
Difference: $68/year
$10,000 Savings at 4% Nominal Rate:
Annual compounding: 4.00% EIR ($400 interest)
Daily compounding: 4.08% EIR ($408 interest)
Difference: $8/year
Final Thoughts
The EIR is the only way to fairly compare financial products. Always:
Ask lenders for EIR (not just APR)
Check compounding frequency
Calculate long-term costs/returns
Need help calculating your EIR? Share your nominal rate and compounding details below! 💰🔍