1. What is Annual Effective Interest Rate?

The Annual Effective Interest Rate (AEIR) is the actual interest rate that is earned or paid on an investment, loan or other financial product due to compounding over a given period. It provides a more accurate measure of true financial cost or return than the nominal rate.

2. How Does the Calculator Work?

The calculator uses the AEIR formula:

Where:

• \( r \) — Nominal interest rate (in decimal form)
• \( m \) — Number of compounding periods per year

Explanation: The formula accounts for the effect of compounding by raising the periodic rate to the power of the number of compounding periods.

3. Importance of AEIR Calculation

Details: AEIR allows for accurate comparison between financial products with different compounding frequencies. It's essential for understanding the true cost of loans or true return on investments.

4. Using the Calculator

Tips: Enter nominal rate as a decimal (e.g., 0.05 for 5%), and the number of compounding periods per year (e.g., 12 for monthly). Both values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between nominal and effective rate?
A: Nominal rate doesn't account for compounding, while effective rate does. The more frequent the compounding, the greater the difference.

Q2: How do I convert percentage to decimal?
A: Divide the percentage by 100 (e.g., 5% becomes 0.05).

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

Q4: Can AEIR be negative?
A: Yes, if the nominal rate is negative, though this is uncommon.

Q5: How does continuous compounding work?
A: As m approaches infinity, the formula becomes e^r - 1 (where e is Euler's number).