1. What is Effective Interest Rate (EIR)?

The Effective Interest Rate (EIR), also known as the Annual Equivalent Rate (AER) or Annual Percentage Yield (APY), is the actual interest rate that an investor earns or pays in a year after accounting for compounding.

2. How Does the Calculator Work?

The calculator uses the EIR formula:

Where:

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

Explanation: The formula accounts for the effect of compounding, showing the true cost or return of a financial product.

3. Importance of EIR Calculation

Details: EIR is crucial for comparing different financial products with varying compounding frequencies, as it standardizes the comparison to an annual rate with compounding.

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 nominal and effective rate?
A: The nominal rate doesn't account for compounding, while the effective rate does. EIR is always equal to or higher than the nominal rate.

Q2: How does compounding frequency affect EIR?
A: More frequent compounding results in a higher EIR for the same nominal rate. Daily compounding gives a higher EIR than monthly, which is higher than annual.

Q3: When is EIR used in finance?
A: EIR is used to compare loans, savings accounts, and investments with different compounding periods. It's required by truth-in-lending laws.

Q4: What's the EIR for continuous compounding?
A: For continuous compounding, use \( e^{nominal} - 1 \) where e is Euler's number (~2.71828).

Q5: Can EIR be lower than nominal rate?
A: No, EIR is always equal to or greater than the nominal rate when compounding occurs more than once per year.