1. What is the EAR Formula?

The EAR (Effective Annual Rate) formula calculates the actual interest rate when compounding is taken into account. It provides a way to compare different investment or loan options with varying compounding periods.

2. How Does the Calculator Work?

The calculator uses the EAR formula:

Where:

• \( Nominal\ Rate \) — Stated annual interest rate (in decimal form)
• \( Periods \) — Number of compounding periods per year

Explanation: The formula accounts for the effect of compounding by showing the actual annual rate when interest is compounded multiple times per year.

3. Importance of EAR Calculation

Details: EAR is crucial for comparing financial products with different compounding frequencies. It shows the true cost of a loan or true return on an investment.

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. Both values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is EAR different from nominal rate?
A: EAR includes compounding effects while nominal rate doesn't. More frequent compounding leads to higher EAR than nominal rate.

Q2: What's the difference between EAR and APR?
A: APR is the nominal rate (doesn't include compounding), while EAR is the actual rate including compounding effects.

Q3: When is EAR equal to nominal rate?
A: Only when compounding occurs exactly once per year (annual compounding).

Q4: How does continuous compounding work?
A: For continuous compounding, use the formula \( EAR = e^{Nominal\ Rate} - 1 \) where e is Euler's number (~2.71828).

Q5: What are typical compounding periods?
A: Common periods are annual (1), semi-annual (2), quarterly (4), monthly (12), weekly (52), and daily (365).