1. What is the Effective Annual Rate (EAR)?

The Effective Annual Rate (EAR) is the actual interest rate that an investor earns or pays in a year after accounting for compounding. For continuous compounding, it's calculated using the exponential function.

2. How Does the Calculator Work?

The calculator uses the continuous compounding formula:

Where:

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

Explanation: This formula accounts for the effect of continuous compounding, which results in the highest possible EAR for a given nominal rate.

3. Importance of EAR Calculation

Details: EAR provides a true comparison of financial products with different compounding periods. It's essential for investment decisions, loan comparisons, and financial planning.

4. Using the Calculator

Tips: Enter the nominal annual interest rate as a decimal (e.g., 0.05 for 5%). The calculator will compute the EAR for continuous compounding.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between APR and EAR?
A: APR is the nominal rate without compounding, while EAR includes compounding effects. EAR gives the true cost/return.

Q2: When is continuous compounding used?
A: In theoretical finance, certain investments, and when compounding occurs constantly rather than at discrete intervals.

Q3: How does continuous compounding compare to daily/monthly?
A: Continuous compounding gives slightly higher returns than daily compounding, with the difference becoming more significant at higher rates.

Q4: Can EAR be negative?
A: Yes, if the nominal rate is negative, though this is rare in practice.

Q5: How to convert EAR back to nominal rate?
A: For continuous compounding: \( r = \ln(1 + EAR) \)