Finance Basics

Loan Payment Formula Explained

Understand the fixed-payment loan formula, monthly interest, amortization and common assumptions behind payment estimates.

This page is for educational calculation only and is not financial advice.

Introduction

A fixed-payment loan usually divides principal and interest into equal scheduled payments. Early payments contain more interest, while later payments generally reduce more principal.

The standard formula estimates principal-and-interest payments when the rate and payment schedule remain constant.

Key concept

For a monthly schedule, M = P × i(1 + i)^n ÷ ((1 + i)^n − 1). P is the principal, i is the monthly interest rate and n is the number of monthly payments.

Formula example

For a $10,000 balance, a 6% nominal annual rate and 36 monthly payments, i is 0.06 ÷ 12 and n is 36. The estimated principal-and-interest payment is about $304.22 per month.

The total of scheduled payments is not the same as the borrowed principal because it includes estimated interest.

Common mistakes

Do not use the annual percentage directly as the monthly rate. Convert the percentage to a decimal and divide by 12 for a monthly schedule.

A basic formula may exclude origination fees, insurance, taxes, variable rates, penalties and other contract terms.

Using an estimate responsibly

Use the result to explore mathematical scenarios and compare input assumptions. Refer to the lender's documents for actual payment obligations and costs.