Amortization Formula Explained — How Your Loan Payment and Interest Are Calculated

Direct Answer

Free amortization calculator: Build an interactive amortization table, chart, and schedule with your loan amount, rate, and term. Export to CSV or PDF. Add optional extra payments, then layer property taxes, homeowners insurance, and PMI for a full amortization schedule with taxes and insurance or amortization schedule with PMI.

The standard formula is:

M = P * r(1 + r)^n / ((1 + r)^n - 1)

Where:

• M = monthly payment
• P = loan principal
• r = monthly interest rate
• n = total number of payments

Calculation note: This article uses the standard fixed-rate amortization equation for principal and interest. It does not include taxes, insurance, fees, or variable-rate adjustments.

Last verified on: June 21, 2026

Editorial note: This guide explains the fixed-payment amortization formula for educational purposes. It covers principal-and-interest math only and does not constitute financial advice.

Research method: Analysis of standard fixed-rate amortization formulas and calculator output checks against common loan-payment examples.

What Each Part Of The Formula Means

The amortization formula looks intimidating because it solves two things at once:

• the interest charged each month
• the principal reduction needed to finish on time

Here is what each variable does.

Principal: P

Principal is the amount borrowed.

If you borrow $25,000, then:

P = 25,000

Monthly Interest Rate: r

The formula uses a monthly interest rate, not the annual rate.

To convert APR (Annual Percentage Rate) to monthly rate:

r = annual rate / 12

For 6% APR:

r = 0.06 / 12
r = 0.005

Number Of Payments: n

The number of payments is the term in months.

Examples:

Worked Example

Assume:

• loan amount: $25,000
• APR: 6%
• term: 5 years
• payment frequency: monthly

Convert the values:

P = 25,000
r = 0.06 / 12 = 0.005
n = 60

Put them into the formula:

M = 25,000 * 0.005(1 + 0.005)^60 / ((1 + 0.005)^60 - 1)

The estimated monthly principal-and-interest payment is about:

M = $483.32

That payment is fixed, but the split between principal and interest changes each month.

How The First Payment Is Split

The first month’s interest is based on the starting balance:

interest = 25,000 * 0.005
interest = $125.00

If the payment is $483.32, the principal portion is:

principal = 483.32 - 125.00
principal = $358.32

After the first payment, the remaining balance is:

balance = 25,000 - 358.32
balance = $24,641.68

Next month, interest is calculated on the lower balance. That is why the interest portion gradually shrinks.

Why The Formula Does Not Show The Whole Schedule

The formula gives the fixed payment, but it does not show every monthly row by itself.

To build an amortization schedule, repeat these steps for each payment:

1. Calculate interest on the current balance.
2. Subtract interest from the payment to get principal.
3. Subtract principal from the balance.
4. Repeat until the balance reaches zero.

That process produces the table most people call an amortization schedule — the same output searchers look for when they want an amortization schedule with extra payments, an amortization schedule with taxes and insurance, or an amortization schedule with PMI.

For a row-by-row walkthrough, see this amortization schedule example.

Common Amortization Schedule Variations

Most borrowers search for one of three extensions to the basic formula:

The Amortization Calculator handles all three: run the monthly payment formula, export the full amortization table and amortization chart, then add extra payments, taxes, insurance, and PMI in one workflow.

Zero-Interest Loan Formula

If the interest rate is 0%, do not use the full formula because the denominator becomes zero.

Use the simpler version:

payment = principal / number of payments

For a $12,000 loan over 24 months:

payment = 12,000 / 24
payment = $500

What The Formula Does Not Include

The basic loan amortization formula calculates principal and interest only.

It does not include:

• property taxes
• homeowners insurance
• PMI (Private Mortgage Insurance)
• origination fees
• late fees
• escrow shortages
• variable interest-rate changes

For mortgages, those extra costs can make the actual monthly payment higher than the amortized principal-and-interest payment.

Extra principal payments also sit outside the base formula. They reduce the balance after the scheduled payment, so the payoff timeline can shorten even when the required payment stays the same. See extra payments on a loan for a worked comparison.

Calculator Methodology

The standard fixed-rate amortization formula:

Monthly P&I = P x r(1 + r)^n / ((1 + r)^n - 1)

Where:

• P is the loan principal
• r is the monthly interest rate (annual rate / 12)
• n is the number of monthly payments (loan term in years x 12)

Assumptions the calculator uses:

• 30-year fixed-rate term (adjustable)
• Interest rate based on current market conditions
• Monthly compounding
• Extra payments (optional) applied directly to principal

What the calculator does not include: Property taxes, homeowners insurance, PMI, homeowners association (HOA) dues, or closing costs. The calculator provides educational estimates only and does not replace a lender’s official amortization schedule or loan offer.

Key Takeaways

The amortization formula calculates the fixed payment needed to repay a loan over a set term. The most important inputs are principal, monthly interest rate, and number of payments.

If you want the payment and the full amortization table and amortization chart, use the Amortization Calculator to see each month’s interest, principal, and remaining balance — with optional extra payments and PMI.

Related Reading

• Car Loan Amortization Schedule Explained — same formula applied to auto loans
• Extra Payments Amortization Schedule — how additional principal changes the table
• Amortization Schedule Example — Table Guide — read a payment table column by column

Official and Supporting Sources

• Consumer Financial Protection Bureau — Understand Loan Costs
• CFPB — How to Read Your Mortgage Statement
• Daily Calcs Amortization Calculator