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

The Effective Annual Rate (EAR) represents the actual annual interest rate when compounding occurs more than once per year. It provides a true comparison of different financial products with varying compounding frequencies.

2. How Does the Calculator Work?

The calculator uses the EAR formula:

Where:

• \( APR \) — Annual Percentage Rate (as a decimal)
• \( n \) — Number of compounding periods per year
• \( EAR \) — Effective Annual Rate (as a decimal)

Explanation: The formula accounts for the effect of compounding by calculating the interest earned on previously accumulated interest over multiple periods.

3. Importance of EAR Calculation

Details: EAR is crucial for comparing different financial products like loans, savings accounts, and investments that have the same APR but different compounding frequencies. It provides the true cost of borrowing or true return on investment.

4. Using the Calculator

Tips: Enter APR as a percentage (e.g., 5 for 5%), and the number of compounding periods per year (e.g., 12 for monthly, 4 for quarterly, 2 for semi-annually). All values must be valid (APR ≥ 0, n ≥ 1).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between APR and EAR?
A: APR is the stated annual rate without considering compounding, while EAR includes the effects of compounding frequency to show the actual annual rate.

Q2: When is EAR higher than APR?
A: EAR is always equal to or higher than APR. The difference increases with more frequent compounding periods.

Q3: What are common compounding frequencies?
A: Annual (n=1), Semi-annual (n=2), Quarterly (n=4), Monthly (n=12), Weekly (n=52), Daily (n=365).

Q4: Why is EAR important for borrowers?
A: It shows the true cost of loans when comparing offers with different compounding frequencies, helping borrowers make informed decisions.

Q5: How does continuous compounding affect EAR?
A: For continuous compounding, use the formula EAR = e^(APR) - 1, where e is Euler's number (approximately 2.71828).