📘 Overview: Effective Annual Rate (EAR) Calculator
The Effective Annual Rate (EAR) Calculator lets you calculate the true annual return or cost of an investment, savings account, or loan — accounting for compounding frequency. Unlike nominal interest rates, which ignore compounding, EAR reflects the actual annualized rate earned or paid.
This tool is essential when comparing financial products with different compounding intervals (e.g., daily vs. monthly vs. annually). A nominal rate may appear attractive, but the compounding frequency determines its real value.
The calculator also includes a comparison chart to visually demonstrate how compounding frequency influences the effective annual rate. More frequent compounding = higher EAR.
📐 Formula & Methodology: How EAR Is Calculated
The formula for converting a nominal interest rate into an effective annual rate is:
EAR = (1 + i/n)n − 1
- i = Nominal annual interest rate (in decimal)
- n = Number of compounding periods per year
To express EAR as a percentage, multiply the result by 100. For instance, if i = 0.12 (12%) and compounding is monthly (n = 12), then:
EAR = (1 + 0.12 / 12)12 − 1 ≈ 0.1268 → 12.68%
EAR captures the time value of money by accounting for interest-on-interest effects, making it a reliable comparison tool for financial decision-making.
🧪 Example Calculations
- Nominal Rate: 6%, Compounded Quarterly (n = 4)
EAR = (1 + 0.06/4)4 − 1 ≈ 6.14% - Nominal Rate: 10%, Compounded Monthly (n = 12)
EAR = (1 + 0.10/12)12 − 1 ≈ 10.47% - Nominal Rate: 5%, Compounded Daily (n = 365)
EAR = (1 + 0.05/365)365 − 1 ≈ 5.13%
📈 Chart Insight: EAR vs. Compounding Frequency
The visual chart shows how EAR increases as compounding becomes more frequent — from annual to monthly to daily. Even if the nominal rate stays constant, the effective return or cost grows due to more compounding intervals.
This is particularly helpful when comparing:
- 💸 Loan offers from banks with different compounding terms
- 📈 Savings or investment products (e.g., CDs vs. daily-yield savings)
- 🏦 Fixed deposits or bond investments
💡 Common Use Cases for EAR Calculations
- 📝 Compare interest-bearing accounts (savings, CDs, money market funds)
- 🔍 Assess true loan costs across banks or credit cards
- 📊 Evaluate investment performance on a consistent annualized basis
- 📚 Learn financial math and compounding behavior in courses
- 📉 Convert nominal interest rates into real, comparable values
❓ Frequently Asked Questions (FAQ)
What is the difference between EAR and APR?
APR (Annual Percentage Rate) typically excludes the impact of compounding, while EAR includes it. EAR gives a more realistic annualized return or cost, especially for frequent compounding.
When should I use EAR?
Use EAR to compare financial products that differ in compounding frequency. It’s useful for credit card APRs, savings rates, investment analysis, and loan comparisons.
Does EAR include fees or taxes?
No. EAR only reflects interest and compounding. It does not account for fees, taxes, or penalties — you should factor those separately.
What does the EAR vs. frequency chart show?
It illustrates how more frequent compounding results in a higher effective annual rate, even with the same nominal rate. It’s a visual way to understand compounding effects.
Can EAR ever equal the nominal rate?
Yes — if compounding is done annually (n = 1), then EAR = nominal rate. More frequent compounding always increases the EAR above the nominal rate.
Is this calculator mobile and tablet friendly?
Absolutely. It works across all devices and is fully responsive — no app or registration required.
Can I use this tool for any currency?
Yes. EAR is a percentage-based result and is currency-agnostic. The output is valid for $, €, ₹, £, ¥, etc.