📊 APR Calculator

Loan Details
Loan Amount ($)
Stated Annual Interest Rate (%)
Loan Term
Fees & Closing Costs
Total Fees & Closing Costs ($)
Results
Monthly Payment --
Total Interest Paid --
Total Cost of Loan (Principal + Interest) --
Stated Interest Rate --
Effective APR --

What is an APR Calculator?

An APR calculator is a financial tool that computes the true annual percentage rate of a loan by factoring in the stated interest rate plus all fees and closing costs. Unlike the simple interest rate, the APR reflects the total cost of borrowing on an annualized basis. This APR calculator helps borrowers compare loan offers accurately by showing the effective rate they will actually pay after accounting for origination fees, points, and other lender charges.

How to Calculate APR

The APR is calculated by finding the discount rate that makes the present value of all future loan payments equal to the net loan proceeds (loan amount minus fees). This requires an iterative numerical method because there is no closed-form algebraic solution.

Loan Amount - Fees = Σ (Monthly Payment / (1 + r)^t) Where: r = Monthly APR (to be solved) t = Payment number (1, 2, ..., n) n = Total number of monthly payments APR = r × 12 × 100

The APR calculator uses the Newton-Raphson method to iteratively solve for the monthly rate r. The process starts with an initial guess and refines it until the present value of payments matches the net loan proceeds within a tight tolerance. The result is annualized and expressed as a percentage.

Key Factors Affecting APR

Stated Interest Rate

The stated interest rate is the base cost of borrowing the principal. It is the rate used to calculate the monthly payment. The APR calculator uses this rate to compute the fixed monthly payment, then determines the APR by factoring in all additional costs.

Loan Amount

The loan amount is the total principal borrowed. A larger loan amount spreads the impact of fixed fees over a larger base, which can reduce the APR relative to the stated rate. The APR calculator shows how the loan amount interacts with fees to determine the final APR.

Fees and Closing Costs

Fees and closing costs are the primary reason the APR differs from the stated interest rate. These include origination fees, discount points, underwriting fees, and other lender charges. The APR calculator adds all fees to compute the true annualized cost of the loan.

Loan Term

The loan term affects how fees are amortized over time. With a shorter loan term, the same fees result in a larger APR increase because the costs are spread over fewer years. The APR calculator allows you to compare APRs across different loan terms to see this effect.

Frequently Asked Questions

What is APR and how is it different from the interest rate?

APR (Annual Percentage Rate) is the true yearly cost of borrowing that includes the stated interest rate plus all fees and closing costs. The interest rate only reflects the cost of borrowing the principal. APR is always equal to or higher than the stated interest rate. This APR calculator shows both figures side by side so you can see the difference.

How is APR calculated?

APR is calculated by finding the discount rate that makes the present value of all loan payments equal to the net amount received (loan amount minus fees). The APR calculator uses an iterative Newton-Raphson method to solve this equation, producing a precise APR that accounts for all loan costs.

Why is APR higher than the interest rate?

APR is higher than the interest rate because it includes additional costs beyond the base interest. When you pay origination fees, discount points, or other closing costs, you effectively receive less money but repay based on the full loan amount. The APR calculator captures this difference and expresses it as a higher annual percentage rate.

What fees are included in APR?

APR typically includes origination fees, discount points, mortgage insurance premiums, underwriting fees, and certain closing costs required by the lender. It does not generally include third-party costs such as title insurance, appraisal fees, or credit report fees. Enter the total of all applicable lender fees into the APR calculator to get an accurate result.