1. What is the 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 form)
• \( n \) — Number of compounding periods per year

Explanation: The formula accounts for the effect of compounding interest, showing the true 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 periods. It helps investors and borrowers understand the true cost or return of financial products.

4. Using the Calculator

Tips: Enter the nominal interest rate as a decimal (e.g., 0.05 for 5%) and the number of compounding periods per year. All values must be valid (nominal rate ≥ 0, compounds ≥ 1).

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 results in a higher EAR. For example, monthly compounding yields a higher EAR than annual compounding at the same nominal rate.

Q3: What are typical compounding periods?
A: Common periods include annually (1), semiannually (2), quarterly (4), monthly (12), weekly (52), and daily (365).

Q4: When is EAR most important to consider?
A: EAR is particularly important when comparing loans or investments with different compounding periods or when compounding is frequent.

Q5: How can I convert EAR back to nominal rate?
A: The nominal rate can be calculated as \( n \times \left(\sqrt[n]{1 + EAR} - 1\right) \), where n is the compounding frequency.