1. What is Effective Annual Interest Rate?

The Effective Annual Interest Rate (EAIR) is the actual interest rate that an investor earns or pays in a year after accounting for compounding. It provides a way to compare different compounding periods on a uniform basis.

2. How Does the Calculator Work?

The calculator uses the EAIR equation:

Where:

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

Explanation: The equation accounts for the effect of compounding interest more frequently than annually, which increases the effective rate.

3. Importance of EAIR Calculation

Details: EAIR is crucial for comparing different financial products with varying compounding periods, helping investors and borrowers understand the true cost or return of financial instruments.

4. Using the Calculator

Tips: Enter nominal rate as a decimal (e.g., 5% = 0.05) and the number of compounding periods per year (e.g., monthly = 12, quarterly = 4). All values must be valid (rate > 0, compounding periods ≥ 1).

5. Frequently Asked Questions (FAQ)

Q1: Why is EAIR different from nominal rate?
A: EAIR includes compounding effects while nominal rate doesn't. The more frequent the compounding, the higher the EAIR compared to nominal rate.

Q2: What's the difference between APR and EAIR?
A: APR is typically the nominal rate, while EAIR reflects the true cost including compounding. EAIR is generally higher than APR.

Q3: How does continuous compounding work?
A: For continuous compounding, use the formula \( e^r - 1 \) where e is Euler's number (~2.71828).

Q4: When is EAIR most important?
A: When comparing loans or investments with different compounding periods, or when compounding occurs more frequently than annually.

Q5: Can EAIR be lower than nominal rate?
A: No, EAIR is always equal to or greater than the nominal rate due to compounding effects.