The amortization formula
A fixed-rate installment loan uses one formula to keep every monthly payment equal while gradually paying down the balance. It looks intimidating but rests on three inputs you already know: principal, rate, and number of payments.
M = P × r × (1 + r)n ÷ ((1 + r)n − 1)
M = monthly payment · P = principal · r = monthly interest rate (annual APR ÷ 12) · n = total number of monthly payments.
A worked example, step by step
Suppose you borrow $2,000 at an 18% APR over 24 months. Here is how the numbers come together:
- Monthly rate r = 18% ÷ 12 = 0.015
- Number of payments n = 24
- Apply the formula → monthly payment M ≈ $99.85
- Total paid = $99.85 × 24 ≈ $2,396
- Total interest = $2,396 − $2,000 ≈ $396
So a $2,000 loan costs roughly $396 in interest over two years at this rate. The same loan over 12 months would have a higher monthly payment but lower total interest — the trade-off explained in how loans work.
Comparing terms at a glance
This static reference table shows how the same $2,000 principal behaves at different terms and rates. It is illustrative only — not a quote.
| APR | Term | Monthly payment | Total interest | Total repaid |
|---|---|---|---|---|
| 10% | 12 mo | $175.83 | $110 | $2,110 |
| 10% | 24 mo | $92.29 | $215 | $2,215 |
| 18% | 12 mo | $183.36 | $200 | $2,200 |
| 18% | 24 mo | $99.85 | $396 | $2,396 |
| 28% | 24 mo | $109.99 | $640 | $2,640 |
Figures are rounded for illustration. Real offers depend on the lender, your credit profile, and fees not shown here.
Why APR is the number that matters
Two loans with identical monthly payments can cost very different amounts once fees are included. APR exists precisely to fold those fees into one comparable figure. When you evaluate any real offer, compare the APR and the total repaid, not just the monthly payment — a low payment stretched over a long term can quietly cost the most.
Before you borrow anything, check
- Does the monthly payment fit your budget without straining essentials?
- What is the total you will repay, including all fees?
- Is there a cheaper alternative — a payment plan, a credit union, or waiting?
- Can you repay early without a penalty if your situation improves?
Frequently asked questions
Is this a loan application or approval tool?
No. This page is an educational explainer of the math behind loan repayment. There is no application, no form that submits to a lender, and nothing here is an offer of credit.
How is a monthly loan payment calculated?
Fixed-rate installment payments use the standard amortization formula, which spreads principal and interest evenly across the term. The page walks through the formula and a worked example.
Why do I pay more total interest on a longer term?
A longer term means you owe the balance for more months, so interest accrues over a longer period. Lower monthly payments often come at the cost of higher total interest.
This page explains how borrowing works so you can make informed choices. We are not a lender or broker, there is no application here, and nothing on this page is a loan offer or financial advice.