1. What is Effective Annual Rate (EAR)?

The Effective Annual Rate (EAR) 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 investment or loan options with different compounding periods.

2. How Does the Calculator Work?

The calculator uses the EAR formula:

Where:

• \( i \) — Nominal interest rate (in decimal)
• \( n \) — Number of compounding periods per year

Explanation: The formula accounts for the effect of compounding by showing how interest earned on interest increases the effective rate.

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, allowing for apples-to-apples comparisons.

4. Using the Calculator

Tips: Enter the nominal interest rate as a percentage (e.g., 5 for 5%) and the number of compounding periods per year (e.g., 12 for monthly compounding).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between APR and EAR?
A: APR (Annual Percentage Rate) doesn't account for compounding, while EAR does. EAR gives the true annual rate when compounding is considered.

Q2: How does compounding frequency affect EAR?
A: More frequent compounding leads to higher EAR. For example, 5% compounded quarterly will have higher EAR than 5% compounded annually.

Q3: What's the EAR for continuous compounding?
A: For continuous compounding, use the formula \( EAR = e^i - 1 \) where e is Euler's number (~2.71828).

Q4: Can EAR be lower than nominal rate?
A: No, EAR is always equal to or greater than the nominal rate, with equality only when compounding occurs annually.

Q5: How is EAR used in financial decisions?
A: Investors use EAR to compare returns on investments with different compounding periods. Borrowers use it to compare loan costs.