Mortgage Calculator

A worked example, before anything else

Suppose you are buying a $400,000 home, putting 20% down, and financing the remaining $320,000 over 30 years at a 6.5% fixed rate. Drop those three numbers into the calculator above and you get a monthly principal-and-interest payment of about $2,022. Over the full 30 years, you will pay roughly $728,000 — meaning the bank will collect about $408,000 in interest on top of the $320,000 you borrowed. The interest, in other words, is bigger than the loan.

That last sentence is the one that surprises people. The total-interest figure the calculator reports is not a footnote; on a 30-year mortgage at typical 2020s rates, it is the dominant cost of the house. If you do nothing else with this calculator, run your own numbers and look at total interest paid, not just the monthly payment.

What this calculator does not include

The number above is principal plus interest only. Three other line items typically appear on a real monthly mortgage statement, and skipping them is the most common way budgets break after the keys are handed over:

• Property taxes. Usually 0.5%–2.5% of the home's assessed value per year, paid monthly through escrow. On a $400,000 home in a 1.2% jurisdiction, that is roughly $400/month — on top of the $2,022.
• Homeowners insurance. Typically $1,000–$2,500 per year depending on geography and risk.
• PMI if your down payment is under 20%. Often 0.5%–1.5% of the loan amount annually, until you cross 20% equity.

For a sharper picture of what you can actually carry, the home affordability calculator factors taxes, insurance, and existing debts into the answer. For points-vs-no-points trade-offs, the amortization calculator breaks down the schedule month by month.

The math, in one paragraph

The monthly payment M on a fixed-rate, fully-amortizing mortgage of principal P, monthly rate r (the annual rate divided by 12), over n total monthly payments (years times 12) is M = P · r · (1 + r)ⁿ / ((1 + r)ⁿ − 1). The denominator is the present-value-annuity factor; the numerator scales it by the principal. Every payment splits into "interest accrued on the remaining balance this month" plus "the rest goes to principal." Early in the loan, almost all of it is interest. Late in the loan, almost all of it is principal. That asymmetry is why mortgage payoff acceleration in the early years compounds dramatically — a $200 extra-payment in year three saves more interest than the same $200 in year twenty-five.

Two questions worth asking before you sign

Should I take a 15-year or a 30-year?

On the same $320,000 loan at 6.5%, a 15-year term raises the monthly payment to about $2,788 — roughly 38% more — but the total interest drops from ~$408,000 to ~$182,000. Less than half. A 15-year mortgage is not a discount; it is a forced-savings plan paid for with monthly liquidity. The defensible reason to take a 30 is that you would otherwise invest the difference at a higher after-tax return than the mortgage rate. If you would not actually invest the difference — most people do not, honestly — the 15 is the cheaper house.

Should I buy points?

A discount point is 1% of the loan amount paid up front in exchange for a permanent rate reduction, usually 0.25%. On a $320,000 loan, one point costs $3,200. If it drops your rate from 6.5% to 6.25%, the monthly savings are about $54. You break even at $3,200 / $54 ≈ 60 months. Points are worth it if you are confident you will stay in the house — without refinancing — for longer than the break-even. Most people in the US move or refinance within 7-10 years, so the math is closer than the lender's sales pitch suggests. Run the break-even, ignore the marketing.

If rates drop after I close?

The refinance calculator compares the closing costs of a refinance against the lifetime interest savings. The rule of thumb — refinance if you can drop the rate by at least 0.75% — is a useful shortcut but ignores the closing costs, which can be $3,000–$8,000. Always run your actual closing-cost estimate against the actual monthly savings.