Professional APR Calculator
Calculate the effective Annual Percentage Rate including all finance charges.
Estimated Annual Percentage Rate
Understanding How APR is Calculated
The Annual Percentage Rate (APR) is a broader measure of the cost to you of borrowing money than the nominal interest rate. The APR reflects the nominal rate, plus other costs such as points, mortgage insurance, and most closing costs. This provides a more accurate picture of the total yearly cost of a loan.
The Difference: Nominal Rate vs. APR
While the nominal rate determines your actual monthly payment, the APR is used as a comparison tool. If you are comparing two loans, one might have a lower nominal rate but significantly higher fees, making the APR higher. The APR represents the "true" price of the credit.
The Mathematical Logic
To calculate APR, we solve for the interest rate that equates the present value of all future payments to the net amount of money received by the borrower (Total Loan Amount minus Upfront Costs). Because this involves complex exponentiation, it is usually solved via an iterative numerical method like the Newton-Raphson process.
| Component | Included in APR? | Description |
|---|---|---|
| Nominal Rate | Yes | The base percentage charged by the lender. |
| Origination Fees | Yes | Cost charged by the lender to process the loan. |
| Discount Points | Yes | Fees paid to lower the interest rate. |
| Appraisal/Credit Report | Usually No | Third-party costs often excluded from APR. |
Real-World Example
Imagine you borrow $100,000 for 30 years (360 months) at a nominal rate of 6%. Your lender charges $4,000 in upfront fees. Your monthly payment is calculated based on the $100,000, but you only "receive" $96,000 after paying the fees. The APR would be approximately 6.39%, representing the higher effective cost of the $96,000 you actually took home.