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Loan Amortization Math

Mortgage Amortization Calculator

Generate a detailed schedule showing how your monthly payments are split between principal and interest over the life of your mortgage.

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Enter your mortgage loan amount, interest rate, term length, and any planned extra monthly or annual payments to build your amortization schedule.
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Understanding Amortization, Principal-Interest Splits, and Payoff Acceleration

Amortization is the process of paying off a debt over time through regular, equal installments. An amortization schedule provides a comprehensive table showing how each of your monthly payments is allocated between paying down the loan balance (principal) and covering the lender's interest fees.

How Amortization Works

For a standard fixed-rate mortgage, your total monthly payment remains constant. However, the ratio of interest to principal shifts with every payment. In the early years of the mortgage, the outstanding balance is high, so the majority of your payment goes toward paying interest. As you make payments and reduce the principal, the interest due decreases, and a larger portion of each payment goes toward reducing the balance.

To see how this applies to a standard home loan, check our comprehensive primary mortgage calculator or check our general standard loan calculator.

The Math Behind the Monthly Payment

The monthly payment is calculated using the following formula: \[M = P \frac{r(1+r)^n}{(1+r)^n - 1}\] Where: - M: The total monthly payment. - P: The principal loan amount. - r: The monthly interest rate (annual interest rate divided by 12). - n: The total number of monthly payments (e.g., 360 for a 30-year loan).

To compare this with refinancing options or modifying an existing loan, check our mortgage refinance calculator.

The Impact of Making Extra Payments

Because amortization is heavily weighted toward interest in the early years, making extra payments can have a dramatic effect. Any additional money paid beyond your required monthly payment is applied directly to your principal loan balance. By reducing the principal faster, you reduce the interest charged in all future months, which shortens your mortgage term and saves you thousands in interest.

To calculate the exact date you can become debt-free by making extra payments, try our mortgage payoff calculator.

Why Review Your Amortization Schedule?

Reviewing your schedule is essential for managing your home equity. Equity is the difference between your home's appraised value and your outstanding mortgage balance. By examining the table, you can see exactly when you will reach key milestones, such as having 20% equity to eliminate private mortgage insurance (PMI) or built-in equity for home renovations.

Equity Building: The Slow Start

New homeowners are often surprised by how slowly they build equity in the first five to ten years of a mortgage. This is due to the front-loaded nature of the amortization schedule. If you plan to sell your home within a short period, you must account for the fact that very little principal has been paid off.

To see how your down payment affects this equity starting point, try our down payment savings tool.

Amortization vs. Depreciation

In accounting, amortization and depreciation refer to spreading costs over time. Amortization is used to spread out the cost of intangible assets (like patents) or loans. Depreciation spreads out the cost of physical assets (like vehicles or machinery) as they wear out.