House Payment Amortization Calculator and Formula

Calculate a level monthly house-loan payment and see the total interest over the full term by entering the loan amount, annual interest rate, and term in years. The calculator assumes a fixed rate and monthly payments; it does not include property taxes, homeowners insurance, mortgage insurance, or escrow costs.

Formula

The fixed monthly payment is calculated with the standard level-payment amortization formula:

Payment = P × r / [1 − (1 + r)⁻ⁿ]

• P is the amount borrowed, in dollars.
• r is the monthly interest rate, found by dividing the annual percentage rate by 1,200. For example, 8% APR gives r = 0.08 / 12, or 0.0066667 per month.
• n is the number of monthly payments: loan term in years × 12.

The calculator rounds the monthly payment to the nearest cent. Total interest is calculated as the rounded payment multiplied by the number of payments, minus the original loan amount. That total assumes every scheduled payment is made and does not account for changes, fees, or extra payments.

Worked Example

Using the calculator’s default values: principal P = $20,000, APR = 8%, and term = 5 years.

1. Convert the APR to a monthly rate: r = 8 / 1,200 = 0.0066667.
2. Find the number of payments: n = 5 × 12 = 60.
3. Substitute into the formula: payment = 20,000 × 0.0066667 / [1 − (1.0066667)⁻⁶⁰].
4. Round the result to cents: monthly payment = $405.53.
5. Calculate total interest using the rounded payment: $405.53 × 60 − $20,000 = $4,331.80.

What Amortization Shows

Amortization is the process of repaying a loan through scheduled payments that cover interest and reduce principal. At the start of a fully amortizing loan, the outstanding balance is larger, so more of each payment goes toward interest. As the balance declines, the interest portion generally shrinks and more of the same scheduled payment reduces principal.

For each month, the basic schedule works like this: multiply the opening balance by the monthly rate to estimate that month’s interest; subtract that interest from the payment to find principal repaid; then subtract the principal portion from the opening balance. For example, on the default loan, first-month interest is about $133.33, leaving about $272.20 of the $405.53 payment to reduce principal. Calculations by a lender may differ by a few cents because of its rounding and payment-processing conventions.

How to Use the Estimate

Enter the amount financed, not necessarily the home’s purchase price. If a down payment reduces the amount borrowed, use the resulting loan principal. Enter the lender’s quoted annual rate as a percentage, such as 6.5 for 6.5%, and enter the term in years. The calculator converts the APR to a monthly rate and multiplies the term by 12.

• Use the loan amount after any down payment or other amount applied at closing.
• Use the rate and term that match the loan offer or scenario you want to examine; the default figures are only a mathematical example.
• Compare the monthly principal-and-interest estimate with a lender’s payment breakdown, checking that the principal, rate, term, and payment frequency match.
• For a variable-rate loan, this result describes only the assumption that the entered rate stays unchanged for the entire term.

The result is not necessarily the full amount due each month for housing. A mortgage statement or estimate may include other charges, such as property taxes, insurance, mortgage insurance, or an escrow deposit. Those items are not inputs here, so add them separately when making a broader monthly cash-flow estimate. Get actual amounts and terms from the relevant documents or service providers.

Common Calculation Issues and Limits

A frequent mistake is entering a percentage as a decimal: enter 8 for 8%, not 0.08. The formula divides the APR by 1,200 because it converts a percent to a decimal and an annual rate to a monthly rate. Another source of confusion is calling every monthly housing expense a mortgage payment. This calculator returns principal and interest only.

The formula assumes a positive APR, a fixed rate, equal monthly payments, and a payment made once per month. It does not model an initial interest-only period, a balloon payment, a changing rate, skipped payments, late charges, closing costs, or additional principal payments. If the loan has a different structure, the level-payment result may not describe its actual schedule.

Rounding matters when reproducing a schedule. The calculator rounds the regular payment to cents before calculating total interest, while a lender’s system may apply its own rounding rules and adjust a final payment. Therefore, the displayed total is a useful formula-based estimate, not a substitute for the lender’s amortization schedule.

Frequently Asked Questions

How do I calculate a house payment with amortization?
Convert the annual percentage rate to a monthly decimal by dividing it by 1,200, convert the term to months, and use P × r / [1 − (1 + r)⁻ⁿ]. P is principal, r is the monthly rate, and n is the payment count.

Does this house payment include taxes and insurance?
No. It estimates principal and interest only. Property taxes, homeowners insurance, mortgage insurance, and escrow amounts are excluded.

How much of each payment goes to principal?
For a given month, subtract that month’s interest from the payment. Interest is the opening balance multiplied by the monthly rate; the remainder is the principal portion.

Why does the interest portion fall over time?
With a fixed rate and a declining loan balance, each later month’s interest is calculated on a smaller amount. The scheduled payment stays level, so the principal portion generally rises.

Can I use this for a variable-rate mortgage?
Only as a single-rate illustration. The calculator assumes the entered APR remains unchanged for every payment and does not forecast future rate adjustments.

Assumptions

• The interest rate is fixed for the full calculated term.
• Payments are equal, made monthly, and applied once per month under a standard amortization schedule.
• Interest compounds monthly at APR / 12.
• Fees, taxes, insurance, mortgage insurance, escrow, and extra payments are not included.

This result is an estimate; the lender’s disclosure gives the exact figures.

Related

• When Is Interest Paid on T-Notes? Payment Dates Explained
• Payments First: Meaning and Loan Payment Calculator
• When Do T-Bills Pay Interest? Payment Timing Explained

in p | Loan amount | $ | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in yrs | Loan term | years | 5 | 0.0833 | 50
out pmt | Monthly payment | $ | p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2