Amortization Calculator

Calculate your loan amortization schedule, view monthly payments, and compare up to three loan scenarios side by side.

Loan A

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Annual Interest Rate (%)

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Use this free amortization calculator to compute your monthly loan payment, view a detailed amortization schedule, and compare up to three loan scenarios side by side.

What Is Amortization?

Amortization is the process of spreading a loan into a series of fixed payments over time. Each payment covers both interest and a portion of the principal balance. In the early stages of the loan, a larger share of each payment goes toward interest; as the balance decreases, more of the payment is applied to principal. By the final payment the loan is fully repaid.

An amortization schedule (also called an amortization table) is a detailed list of every payment over the life of the loan. It shows exactly how much of each payment is interest, how much reduces the principal, and the remaining balance after each period.

This Calculator and the Mortgage Calculator

This amortization calculator and our Mortgage Calculator share the same core calculation engine — the PMT formula, the period-by-period interest and principal split, and the amortization schedule logic are identical between the two.

The difference is focus:

This amortization calculator is the foundational tool. It deals with the pure loan math — enter a loan amount, interest rate, and term, and you get the monthly payment with a full schedule. It also lets you compare up to three loan scenarios side by side. If you want to understand how the calculation works, this is the right place to start. We explain the math step by step below.
The Mortgage Calculator builds on top of the same engine and adds homebuying-specific features: it starts with home price and down payment, layers on optional homeownership costs (property tax, insurance, etc.), and supports extra payments that help you pay off the loan early and see how much interest you save.

If you need extra costs or extra payments, consider using our Mortgage Calculator — it has all the amortization features plus those additional capabilities.

The Idea Behind the Monthly Payment (PMT)

Before we dive into the formula, let's understand the idea behind it — because the math becomes much easier to follow once you see what it is trying to do.

The Core Concept

When you take out a loan, you agree to make a fixed payment every month for a set number of months. That fixed payment needs to accomplish one thing: bring the remaining balance to exactly zero by the last month.

Each month, two things happen:

Interest accrues on whatever balance is still outstanding. If your balance is large, the interest is large; if the balance is small, the interest is small.
After interest is covered, the rest of your payment reduces the principal. This is why early payments are mostly interest (balance is high) and late payments are mostly principal (balance is low).

So the question the PMT formula answers is: *What fixed monthly amount, paid every month for $n$ months, will exactly pay off a principal of $P$ at a monthly interest rate of $r$ ?*

Setting Up the Equation

Let's trace what happens month by month. Call the fixed payment $M$ :

After month 1: The balance grows by interest, then you pay $M$ .

\text{Balance}_1 = P(1 + r) - M

After month 2: Interest accrues on the new balance, then you pay $M$ again.

\text{Balance}_2 = \text{Balance}_1 \cdot (1 + r) - M = P(1+r)^2 - M(1+r) - M

After month $n$ : Following this pattern, the balance is:

\text{Balance}_n = P(1+r)^n - M\left[(1+r)^{n-1} + (1+r)^{n-2} + \cdots + 1\right]

The sum in brackets is a geometric series that simplifies to:

\frac{(1+r)^n - 1}{r}

So the balance after $n$ months is:

\text{Balance}_n = P(1+r)^n - M \cdot \frac{(1+r)^n - 1}{r}

Solving for the Payment

We want the balance to be zero after the last payment: $\text{Balance}_n = 0$ . Setting the equation to zero and solving for $M$ :

P(1+r)^n = M \cdot \frac{(1+r)^n - 1}{r}

M = P \times \frac{r \,(1 + r)^{n}}{(1 + r)^{n} - 1}

This is the PMT formula. It is not an approximation — it is the exact payment that zeros out the loan.

The PMT Formula

PMT = P \times \frac{r \,(1 + r)^{n}}{(1 + r)^{n} - 1}

Where:

$P$ = loan principal (the original amount borrowed)
$r$ = monthly interest rate = annual rate ÷ 12 ÷ 100
$n$ = total number of monthly payments (loan term in months)

Example: For a $200,000 loan at 6% annual interest over 30 years (360 months):

$r = 6 / 12 / 100 = 0.005$
$n = 360$

PMT = 200{,}000 \times \frac{0.005 \times (1.005)^{360}}{(1.005)^{360} - 1} \approx \$1{,}199.10

When the interest rate is 0%, interest never accrues, so the formula simplifies to $PMT = P / n$ .

How Interest and Principal Are Calculated Each Period

For each payment period $k$ :

\text{Interest}_k = \text{Balance}_{k-1} \times r

\text{Principal}_k = PMT - \text{Interest}_k

\text{Balance}_k = \text{Balance}_{k-1} - \text{Principal}_k

Interest is calculated on the current outstanding balance, so it decreases each month as the balance shrinks.
Principal is the remainder of the fixed payment after interest is deducted, so it increases each month.
At the very last payment the remaining balance is paid off in full.

This predictable shift from mostly-interest to mostly-principal is the hallmark of an amortizing loan.

How to Use This Calculator

Enter Loan Details — Input the loan amount, annual interest rate, and loan term (in years or months). The calculator instantly shows your monthly payment, total payment, and total interest.
Select Your Currency — Use the currency selector to display amounts in your preferred currency.
View the Amortization Schedule — Expand the schedule section to see every payment broken down by interest, principal, and remaining balance. Toggle between monthly and yearly views. Green data bars visually illustrate the interest-to-principal ratio for each period.
Compare Multiple Loans — Click the + button to add up to three loan tabs. Each tab has independent inputs and results. Use the comparison charts below to visualize differences in monthly payment, total payment, total interest, and interest rate.

What Makes This Calculator Different

Side-by-side comparison — Most amortization calculators handle only one loan at a time. Here you can compare up to three scenarios with bar charts that update in real time.
Visual schedule with data bars — The amortization table includes green data bars for each row so you can instantly see the interest-to-principal ratio shift over time.
Monthly and yearly toggle — Switch between a detailed month-by-month view and a condensed year-by-year summary with one click.
No sign-up required — All calculations happen in your browser. Your data stays private and nothing is sent to a server.

FAQ

What types of loans use amortization?

Most consumer loans are amortizing: home mortgages, auto loans, personal loans, and student loans. Credit cards and some business lines of credit are typically non-amortizing (revolving credit).

Can the interest rate change during the loan?

This calculator assumes a fixed interest rate for the entire term. If you have an adjustable-rate mortgage (ARM), you can use separate tabs to model different rate scenarios.

Why does the interest portion decrease over time?

Because interest is calculated on the remaining balance. As you pay down principal, the balance decreases, so less interest accrues each period and more of your fixed payment goes toward reducing the principal.

What if I want to model extra payments or homeownership costs?

This calculator focuses on pure amortization with fixed payments. If you need to model extra payments (monthly, yearly, or one-time), or include additional costs like property tax and insurance, our Mortgage Calculator has those features built in — and it uses the same amortization engine under the hood.