1. What is the EAR Formula?

The EAR (Effective Annual Rate) formula converts a stated periodic rate to an annual rate that accounts for compounding. It's particularly useful when comparing investments with different compounding periods.

2. How Does the Calculator Work?

The calculator uses the EAR formula for continuous compounding:

Where:

• \( EAR \) — Effective Annual Rate (decimal)
• \( e \) — Euler's number (~2.71828)
• \( r \) — Periodic interest rate (decimal)

Explanation: The formula shows the annual growth factor when interest is compounded continuously at rate r.

3. Importance of EAR Calculation

Details: EAR allows for accurate comparison between different investment or loan options with varying compounding periods, providing a true annual rate of return or cost.

4. Using the Calculator

Tips: Enter the periodic rate in decimal form (e.g., 0.05 for 5%). The rate should be ≥ 0.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between EAR and APR?
A: APR (Annual Percentage Rate) doesn't account for compounding, while EAR does, making EAR more accurate for comparisons.

Q2: When is continuous compounding used?
A: Continuous compounding is common in theoretical finance and certain investments like money market accounts.

Q3: How do I convert EAR back to periodic rate?
A: Use the natural logarithm: \( r = \ln(1 + EAR) \).

Q4: What's the maximum possible EAR?
A: There's no theoretical maximum, though practical rates are limited by market conditions.

Q5: How does EAR change with compounding frequency?
A: EAR increases with more frequent compounding for the same nominal rate.