Mortgage Amortization Calculator with Extra Payments

A lender quotes you a rate and a principal-and-interest payment, but the amount that leaves your account each month is bigger, and what you hand over across the whole loan is bigger still. This calculator builds both: it derives the fixed payment from your price, down payment, term and rate, adds tax, insurance, PMI and HOA, then walks the loan month by month to a payoff date, a total interest figure and a full amortization schedule.

What the monthly figure is made of

The large number at the top is not your loan payment. It is the sum of every line in the breakdown beside it:

• Principal & interest — the only part fixed by your loan contract, and the only part the amortization formula produces.
• Property tax and home insurance — each entered as a percentage of the home price per year or a flat dollar amount per year, then divided by twelve. The unit button converts the value when you switch.
• PMI — applied only when your down payment is under 20%, as an annual percentage of the original loan amount divided by twelve.
• HOA and other costs — flat monthly amounts passed straight through.
• Extra principal — included when extra payments are switched on, because it genuinely leaves your account.

Only the first line is locked in. Taxes get reassessed, premiums get re-rated and HOA dues get voted up, so year one's payment is not year ten's.

The amortization formula

Principal and interest come from the standard level-payment (annuity) formula:

M = P × i(1 + i)^n / ((1 + i)^n − 1)

P is the amount borrowed (price minus down payment), i is the periodic rate — your annual rate divided by 100, then by 12 — and n is the term in years multiplied by 12. At a rate of zero the tool falls back to P/n, since the formula divides by zero there.

M stays constant, but what it buys does not. Each month the tool charges interest equal to the balance × i, and whatever the payment covers beyond that reduces the balance. Early on the balance is large, so most of the payment is interest. The note under the chart says how long that phase lasts: the first month in which principal overtakes interest.

Reading the chart, schedule and totals

The chart plots three lines by year: the balance falling, interest paid to date rising, and total paid to date rising faster. The schedule below reads annually or, on the Monthly tab, payment by payment with real dates.

In the totals card, total out-of-pocket adds four things: your down payment, the amount borrowed, all the interest, and every tax, insurance, PMI, HOA and other cost charged over the life of the loan. That is the honest answer to "what does this house cost me?", and it is usually the figure that surprises people.

Extra payments and how PMI is dropped

Extra money goes straight against principal, removing the interest that balance would have generated for the rest of the term. Three kinds are modelled: a fixed amount every month, a lump on every twelfth payment, and a one-time sum at the first payment. When any are active the tool runs the loan twice, with and without, and reports the interest saved and how much earlier the balance hits zero.

PMI is handled dynamically rather than as a permanent line: it is charged only while the balance sits above 80% of the original home price, which is why later schedule rows can be cheaper. In the United States the Homeowners Protection Act governs when borrower-paid PMI may be cancelled and when a servicer must end it, measured against the original property value rather than a later appraisal — the PMI removal calculator covers that.

What this model deliberately leaves out

• Closing costs — origination, title, appraisal and prepaids. Estimate them with the closing cost calculator.
• Rate changes — one fixed rate is assumed throughout; adjustable loans need the ARM mortgage calculator.
• Government-backed loan rules — FHA, VA and USDA loans carry their own fees and insurance rules that ignore the 80% cut-off used here.
• Escrow drift and tax treatment — tax and insurance stay flat, and no mortgage interest deduction is applied.

How to use the mortgage calculator

1. Enter the home price, then the down payment; the unit button switches between a percentage and a dollar figure.
2. Set the loan term and the interest rate you have been quoted, then pick the month and year of your first payment so the schedule uses real dates.
3. Leave Include taxes, insurance & fees on and fill in tax, insurance, PMI rate, HOA and other costs — this is what makes the headline figure resemble your outgoings.
4. Read the breakdown and donut to see how much is loan and how much is everything else, then check the totals card for interest, payoff date and out-of-pocket cost.
5. Tick Add extra payments and try a modest monthly amount; the green panel reports the interest saved and time cut from the term.
6. Switch the schedule to Monthly if you need the exact balance at a future date.

Frequently Asked Questions

Why is this higher than the payment my lender quoted?

Lenders usually quote principal and interest only, while this tool adds escrow and household costs by default. Compare like with like by reading the "Principal & interest" line, or unticking the taxes and fees box.

Should I enter the interest rate or the APR?

Enter the note rate, the one used to calculate interest. APR bundles certain fees into a comparison figure and would overstate the monthly interest charge here. The tool has no rate feed; whatever you type is what it uses.

Is a monthly extra better than one lump each year?

Money applied earlier stops more interest, so a monthly extra generally beats the same total paid once a year — often by less than people expect. Enter both and compare the interest saved.

How does the tool decide when PMI stops?

It charges PMI only if taxes and fees are on and the down payment is below 20%, and stops once the balance drops under 80% of the original price. Servicers also require you to be current on payments, so treat the cut-off as an estimate.

Why does a shorter term change total interest so much?

Interest is charged on the balance that remains, so a shorter term keeps that balance high for fewer months and compresses the whole interest curve. The monthly payment rises; total interest can fall by a large multiple.

Can I use it outside the United States?

The arithmetic suits any fixed-rate, level-payment loan, but the PMI logic and terminology are US-specific.

Sources

• Standard level-payment (annuity) amortization formula, M = P × i(1 + i)^n / ((1 + i)^n − 1).
• Homeowners Protection Act (United States) — cancellation and termination of borrower-paid private mortgage insurance, measured against original property value.