1. What is the EAR Equation?

The EAR (Effective Annual Rate) equation calculates the actual annual rate that an investment will earn or a loan will cost when compounding is taken into account. It provides a more accurate measure than the nominal APR (Annual Percentage Rate).

2. How Does the Calculator Work?

The calculator uses the EAR equation:

Where:

• \( APR \) — Annual Percentage Rate (as decimal)
• \( m \) — Number of compounding periods per year

Explanation: The equation accounts for the effect of compounding by showing how more frequent compounding leads to higher effective rates.

3. Importance of EAR Calculation

Details: EAR is crucial for comparing financial products with different compounding periods. It shows the true cost of loans or true return on investments.

4. Using the Calculator

Tips: Enter APR as decimal (e.g., 0.05 for 5%), and the number of compounding periods per year (e.g., 12 for monthly). Both values must be valid (APR ≥ 0, m ≥ 1).

5. Frequently Asked Questions (FAQ)

Q1: Why use EAR instead of APR?
A: EAR accounts for compounding effects, giving a more accurate measure of actual interest costs or returns.

Q2: What's the difference between APR and EAR?
A: APR is the nominal rate without compounding, while EAR includes compounding effects.

Q3: How does compounding frequency affect EAR?
A: More frequent compounding (higher m) results in higher EAR for the same APR.

Q4: What's the maximum possible EAR for a given APR?
A: As m approaches infinity, EAR approaches e^APR - 1 (continuous compounding).

Q5: When is EAR most important?
A: When comparing financial products with different compounding periods or when compounding is frequent.