# APR Calculator Calculate the true Annual Percentage Rate (APR) of a loan when upfront fees are involved. The nominal interest rate sets the monthly payment, but fees reduce the net cash received, raising the effective APR. Uses Newton's method to solve the annuity present-value equation. Shows APR, nominal rate, monthly payment, and the APR premium. > Canonical page: https://elysiatools.com/en/tools/apr-calculator - **Category:** Finance - **Keywords:** apr, annual percentage rate, effective rate, loan fees, true cost of borrowing, newton method, finance, interest rate ## Overview The APR Calculator determines the true Annual Percentage Rate (APR) of a loan by factoring in upfront fees that reduce your net cash received. By using Newton's method to solve the annuity present-value equation, this tool reveals the actual cost of borrowing, displaying the APR, nominal interest rate, monthly payment, and the APR premium. ## Inputs - **Loan Amount** (number): e.g. 20000 - **Nominal Interest Rate (%)** (number): e.g. 6.5 - **Loan Term (Months)** (number): e.g. 60 - **Upfront Fees** (number): e.g. 500 - **Fee Financed (included in loan)** (checkbox) - **Decimal Places** (number) ## When to use - When comparing loan offers from different lenders that have varying upfront fees and nominal interest rates. - When you need to calculate the true cost of borrowing after accounting for origination fees, processing fees, or points. - When deciding whether to finance upfront fees into the loan amount or pay them out of pocket. ## How it works - Enter the total loan amount, nominal interest rate, and the loan term in months. - Input any upfront fees and specify whether these fees are financed (included in the loan) or paid out of pocket. - The calculator uses Newton's method to solve the annuity present-value equation based on the net cash received. - Review the calculated monthly payment, the true APR, and the APR premium showing the impact of the fees. ## Use cases - Comparing a low-interest loan with high upfront fees against a higher-interest loan with zero fees. - Calculating the real interest rate on a car loan that includes dealer preparation and documentation fees. - Evaluating mortgage options where points or origination fees are charged at closing. ## Frequently asked questions ### What is the difference between the nominal interest rate and the APR? The nominal rate determines your monthly payment, while the APR reflects the true annual cost of borrowing by factoring in upfront fees. ### How do upfront fees affect the APR? Upfront fees reduce the net cash you receive, which increases the effective interest rate (APR) you pay on the actual money borrowed. ### What does it mean to finance a fee? Financing a fee means adding the fee amount to the total loan balance, which increases your monthly payment and changes the APR calculation. ### How does the calculator solve for the APR? It uses Newton's method, an iterative numerical technique, to solve the annuity present-value equation for the interest rate. ### What is the APR premium? The APR premium is the difference between the calculated APR and the nominal interest rate, representing the extra cost added by fees. ## Related tools - [Auto Loan Calculator](https://elysiatools.com/en/tools/auto-loan-calculator): Calculate your car loan monthly payment factoring in vehicle price, down payment, trade-in value, sales tax, and registration fees. Shows amount financed, total interest, total cost, a descending balance curve, and a yearly amortization schedule. - [Compound Annual Growth Rate (CAGR) Calculator](https://elysiatools.com/en/tools/compound-annual-growth): Calculate the compound annual growth rate (CAGR) from a beginning value, ending value and number of years; compare with the simple average growth rate and visualize the smooth growth curve. CAGR = (EV/BV)^(1/n) - 1. - [Net Worth Calculator](https://elysiatools.com/en/tools/net-worth-calculator): Calculate your net worth from a list of assets and liabilities (Net Worth = Total Assets − Total Liabilities). 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