Effective Interest Rate Calculator
Calculate the true annual rate accounting for compounding frequency
Calculate Effective Interest Rate
The stated or nominal annual interest rate
Interest compounds at regular intervals
How often interest is compounded per year
Interest Rate Results
Formula used: (1 + r/m)^m - 1 = (1 + 0%/12)^12 - 1
Compounding: Twelve times per year
Future Value Calculation
Rate Analysis
Example Calculation
Credit Card Example
Nominal Rate: 18% annual
Compounding: Monthly (12 times/year)
Periodic Rate: 18% ÷ 12 = 1.5%
Calculation Steps
1. EIR = (1 + 0.18/12)^12 - 1
2. EIR = (1 + 0.015)^12 - 1
3. EIR = (1.015)^12 - 1
4. EIR = 1.1956 - 1
Effective Rate: 19.56%
The extra 1.56% comes from monthly compounding.
Compounding Impact
Annual
No compounding benefit
EIR = Nominal Rate
Monthly
Common for loans/savings
Moderate compounding effect
Continuous
Maximum compounding
Uses natural exponential
Interest Rate Tips
Higher frequency increases effective rate
EIR shows true cost/return of financial products
Compare investments using effective rates
Daily compounding maximizes savings returns
Understanding Effective Interest Rate
What is Effective Interest Rate?
The Effective Interest Rate (EIR) is the true annual rate that accounts for the effect of compounding. It shows what you actually earn or pay when interest is calculated and added to your balance multiple times per year, rather than just once.
Why Use EIR?
- •Compare financial products with different compounding frequencies
- •Understand the true cost of loans and credit cards
- •Evaluate the actual return on savings and investments
- •Make informed financial decisions based on real rates
EIR Formulas
EIR = (1 + r/m)^m - 1
Discrete Compounding
- r: Annual nominal rate (decimal)
- m: Compounding frequency per year
EIR = e^r - 1
Continuous Compounding
- e: Euler's number (≈2.71828)
- r: Annual nominal rate (decimal)
Key Components
Nominal Rate
The stated annual interest rate before compounding
Compounding Frequency
How many times per year interest is calculated and added
Periodic Rate
The interest rate for each compounding period
Compounding Frequency Comparison
| Frequency | Times/Year | 12% Nominal → EIR | Benefit |
|---|---|---|---|
| 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% |