1. What is Semi-Annual Equivalent Rate?

The Semi-Annual Equivalent Rate (Effective Annual Rate) calculates the annual interest rate when interest is compounded semi-annually. It shows the true annual return accounting for compounding effects.

2. How Does the Calculator Work?

The calculator uses the EAR formula for semi-annual compounding:

Where:

• \( EAR \) — Effective Annual Rate (decimal)
• \( r \) — Semi-annual nominal interest rate (decimal)

Explanation: The formula accounts for the compounding effect that occurs when interest is paid twice per year, resulting in a higher effective annual rate than the nominal rate.

3. Importance of EAR Calculation

Details: EAR provides a standardized way to compare investment returns or loan costs with different compounding frequencies. It represents the true annual cost or return of financial products.

4. Using the Calculator

Tips: Enter the semi-annual nominal interest rate as a percentage (e.g., enter 5 for 5%). The calculator will return the effective annual rate as a percentage.

5. Frequently Asked Questions (FAQ)

Q1: Why is EAR higher than the nominal rate?
A: Due to compounding - interest earned in the first period earns additional interest in subsequent periods.

Q2: How does semi-annual compare to other compounding frequencies?
A: Semi-annual compounding results in a higher EAR than annual compounding but lower than quarterly or monthly compounding for the same nominal rate.

Q3: When is semi-annual compounding commonly used?
A: Often used in corporate bonds, government securities, and some savings accounts where interest payments are made twice yearly.

Q4: Can I use this for loan calculations?
A: Yes, EAR helps compare loan costs across different compounding frequencies and nominal rates.

Q5: What's the difference between APR and EAR?
A: APR is the nominal annual rate, while EAR includes compounding effects and represents the true annual cost or return.