Apr Calculator

What is the Annual Percentage Rate (APR)?

The Annual Percentage Rate (APR) is a broader measure of the cost of borrowing money than the interest rate alone. While the interest rate tells you how much interest you pay on the principal balance each month, the APR includes both the interest rate and any additional fees or costs associated with securing the loan.

Common fees factored into the APR include loan origination fees, points, broker fees, and closing costs. Because it incorporates these upfront expenses, the APR is almost always higher than the advertised interest rate.

The Mathematical Formula for APR

The APR is calculated by finding the discount rate that equates the net loan proceeds (the total loan amount minus upfront fees) with the present value of all subsequent monthly payments. The basic relationship is represented by:

Where:

• P is the principal loan amount.
• F is the total upfront fees or closing costs.
• M is the monthly payment based on the base interest rate.
• r_APR is the monthly APR rate (the annual APR divided by 12).
• n is the total number of monthly payments.

Once the monthly rate r_APR is found using numerical methods, the annual percentage rate is calculated as:

Why APR Matters

Comparing loans based purely on interest rates can be misleading. For example, a loan with a lower interest rate but high upfront fees might end up costing more than a loan with a slightly higher interest rate but no fees. The APR translates those upfront fees into an equivalent annual interest rate, giving you a standardized baseline for side-by-side comparisons.