Finance & Economics · Real Estate & Mortgages
Mortgage Calculator
Calculate your monthly mortgage payment, total interest paid, and amortization details based on loan amount, interest rate, and term.
Calculator
Formula
M is the monthly payment, P is the principal loan amount, r is the monthly interest rate (annual rate divided by 12), and n is the total number of payments (loan term in years multiplied by 12).
Source: Federal Reserve Regulation Z — Truth in Lending Act (12 CFR Part 1026), standard amortization formula.
How it works
A mortgage is a fully amortizing loan, meaning each monthly payment is structured to cover both interest accrued since the last payment and a portion of the outstanding principal. Early in the loan's life, the vast majority of each payment goes toward interest because the outstanding balance is high. As you make payments and reduce the principal, the interest portion shrinks and the principal portion grows — this is the core mechanic of amortization.
The formula at the heart of this calculator is M = P · [r(1+r)ⁿ] / [(1+r)ⁿ − 1], where P is the loan principal, r is the monthly interest rate (annual rate ÷ 12), and n is the total number of monthly payments (years × 12). This formula is derived from the present value of an annuity and ensures that, at the end of exactly n payments, the balance reaches zero. The monthly rate is crucial: a 6.5% annual rate becomes 0.5417% per month, and this compounding is what drives the total interest cost.
Understanding the relationship between these three variables is powerful. Extending your term from 15 to 30 years cuts the monthly payment significantly but can more than double the total interest paid. A slightly lower interest rate — even by 0.25% — can save tens of thousands of dollars over a 30-year mortgage. This calculator isolates the principal-and-interest (P&I) component; your actual monthly housing payment will also include property taxes, homeowners insurance, and potentially private mortgage insurance (PMI), which are not included here.
Worked example
Suppose you are purchasing a home and need a loan of $350,000 at an annual interest rate of 6.75% for a term of 30 years.
Step 1 — Convert to monthly rate: r = 6.75% ÷ 12 = 0.5625% = 0.005625 per month.
Step 2 — Calculate number of payments: n = 30 × 12 = 360 payments.
Step 3 — Apply the amortization formula:
M = 350,000 × [0.005625 × (1.005625)³⁶⁰] / [(1.005625)³⁶⁰ − 1]
(1.005625)³⁶⁰ ≈ 7.6883
M = 350,000 × [0.005625 × 7.6883] / [7.6883 − 1]
M = 350,000 × 0.043247 / 6.6883
M = 350,000 × 0.006467
M ≈ $2,263.38 per month
Step 4 — Total cost and interest:
Total Paid = $2,263.38 × 360 = $814,815.71
Total Interest = $814,815.71 − $350,000 = $464,815.71
This means that over the 30-year life of this loan, you will pay back more than double the original loan amount — a powerful illustration of why minimizing your interest rate or shortening your term saves significant money.
Limitations & notes
This calculator computes only the principal-and-interest (P&I) portion of a mortgage payment and does not account for property taxes, homeowners insurance, or private mortgage insurance (PMI), which can add hundreds of dollars per month to your actual payment. It also assumes a fixed interest rate for the entire term; adjustable-rate mortgages (ARMs) will have payments that change after an initial fixed period. The formula does not account for extra principal payments, biweekly payment schedules, or loan origination fees and closing costs, all of which materially affect the true cost of borrowing. Always consult a licensed mortgage professional or HUD-approved housing counselor before making real estate financing decisions.
Frequently asked questions
What does the monthly mortgage payment include?
This calculator's monthly payment covers only principal and interest (P&I) — the two components governed by the loan amortization formula. Your actual monthly housing expense will also include property taxes (typically escrowed), homeowners insurance, and possibly private mortgage insurance (PMI) if your down payment is less than 20% of the home's value. These additional costs vary widely by location and lender.
How does the loan term affect total interest paid?
Loan term has a dramatic effect on total interest. For a $300,000 loan at 6.5%, a 30-year term results in a monthly payment of about $1,896 and roughly $382,600 in total interest, while a 15-year term raises the monthly payment to about $2,613 but reduces total interest to approximately $170,300 — a savings of over $212,000. Shorter terms build equity faster and drastically reduce interest costs, though they require higher monthly cash flow.
What is amortization and why does it matter?
Amortization is the process of gradually paying off a debt through regular scheduled payments over time, with each payment split between interest and principal reduction. In the early years of a mortgage, most of your payment goes to interest; in the later years, most goes to principal. This matters because if you sell or refinance the home in the first few years, you will have paid mostly interest and built relatively little equity, which directly affects your net proceeds.
What is the difference between interest rate and APR?
The interest rate is the cost of borrowing the principal, expressed as an annual percentage, and is what this calculator uses to compute your payment. The Annual Percentage Rate (APR) is a broader measure that includes the interest rate plus lender fees, mortgage points, and other loan costs, expressed as a yearly rate. The APR is always equal to or higher than the interest rate and is a more complete indicator of the true cost of the loan, making it the better metric for comparing offers from different lenders.
Should I choose a 15-year or 30-year mortgage?
The right choice depends on your financial priorities and cash flow. A 30-year mortgage offers lower monthly payments, providing budget flexibility and allowing you to invest the difference — but you pay far more interest over time. A 15-year mortgage builds equity quickly and saves substantially on interest, but demands higher monthly payments, which can strain budgets if income is disrupted. Many financial planners suggest a 30-year mortgage if you invest the payment difference aggressively, and a 15-year if reducing debt is your primary goal.
Last updated: 2025-01-15 · Formula verified against primary sources.