1. What is the APR Formula?

The APR (Annual Percentage Rate) formula calculates the effective annual rate when compounding is taken into account. It provides a more accurate measure of the true cost or return compared to the nominal rate.

2. How Does the Calculator Work?

The calculator uses the APR formula:

Where:

• \( r \) — Nominal interest rate (decimal)
• \( m \) — Number of compounding periods per year

Explanation: The formula accounts for the effect of compounding interest, showing how more frequent compounding leads to higher effective returns.

3. Importance of APR Calculation

Details: Understanding the effective APR is crucial for comparing different savings or loan products, as it standardizes rates with different compounding frequencies.

4. Using the Calculator

Tips: Enter the nominal rate as a decimal (e.g., 0.05 for 5%), and the number of compounding periods per year (e.g., 12 for monthly). Both values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between APR and APY?
A: APR is the annual rate without compounding, while APY (Annual Percentage Yield) includes compounding effects.

Q2: How does compounding frequency affect APR?
A: More frequent compounding (higher m) results in a higher effective APR for the same nominal rate.

Q3: What are typical compounding frequencies?
A: Common frequencies include annual (1), semi-annual (2), quarterly (4), monthly (12), weekly (52), and daily (365).

Q4: Can this formula be used for loans?
A: Yes, it works for both savings and loans to calculate the effective interest rate.

Q5: What's the limit as compounding becomes continuous?
A: As m approaches infinity, the formula approaches e^r - 1 (where e is Euler's number).