How mortgage payments work

Updated April 28, 2026 · 8 min read · by Samuel Yoo

A 30-year fixed-rate mortgage is a contract that says: every month for 360 months, you pay the bank the same amount, and at the end you own the house free and clear. The amount is fixed. What’s inside that amount — how much of each payment goes to interest vs. principal — changes every single month.

This page is the honest version of how that math works. No upsell to a lender, no fluffy explainer. Just the formula, an example, and the interesting consequences.

The PMT formula

The monthly payment on a fixed-rate, fully-amortising loan is:

M = P × [r(1 + r)^n] / [(1 + r)^n − 1]

Where:

• M is the monthly payment (just principal and interest — no tax, insurance, or HOA).
• P is the loan amount: home price minus down payment.
• r is the monthly interest rate, computed as APR / 12. (Yes, mortgages say “annual rate” and compute with a simple monthly twelfth — the difference between that and a true annualised compound rate is small but non-zero.)
• n is the number of monthly payments. 30-year loan ⇒ 360 months.

That’s the whole formula. Every “mortgage calculator” on the internet implements this with a different shade of UI lipstick.

A worked example

Say you’re buying a $500,000 house with $100,000 down at 6.5% APR for 30 years.

• P = $400,000
• r = 0.065 / 12 ≈ 0.005417
• n = 360
• (1 + r)^n ≈ 7.024
• Numerator: 400,000 × 0.005417 × 7.024 ≈ 15,217
• Denominator: 7.024 − 1 = 6.024
• M ≈ $2,528.27

So your monthly principal-and-interest payment is $2,528.27.

Over 360 months, you’ll pay $2,528.27 × 360 = $910,177. Of that, $400,000 is principal (the loan itself) and $510,177 is interest. On a 30-year loan at this rate, you pay the bank more in interest than you borrowed.

Why your first payment is mostly interest

In the first month, the loan balance is the full $400,000. Interest accrues on that balance at the monthly rate:

interest_month_1 = 400,000 × 0.005417 = $2,166.67
principal_month_1 = $2,528.27 − $2,166.67 = $361.60

So of your first $2,528.27 payment, only $361.60 actually pays down the loan. The other 86% is interest. By payment #180 (year 15), the balance has dropped to about $283,000 and the split is roughly 50/50. By payment #360, the balance is near zero and almost the entire payment is principal.

This is what the amortisation schedule looks like in shape:

Payment 1:    $361 principal,  $2,167 interest  (balance: $399,638)
Payment 60:   $499 principal,  $2,029 interest  (balance: $374,038)
Payment 120:  $691 principal,  $1,837 interest  (balance: $338,283)
Payment 180:  $957 principal,  $1,571 interest  (balance: $288,786)
Payment 240: $1,325 principal, $1,203 interest  (balance: $221,225)
Payment 300: $1,835 principal,   $693 interest  (balance: $127,610)
Payment 360: $2,514 principal,    $14 interest  (balance: $0)

The total payment is constant ($2,528.27), but how you allocate it shifts nonlinearly toward principal as the balance drops.

What extra principal actually buys you

Add $200/month in extra principal to that same loan and watch what happens:

• Monthly payment: $2,728.27 (the $2,528.27 P&I + $200 extra)
• Loan paid off: month 290 (instead of 360) — 5 years and 10 months early
• Total interest paid: ~$391,000 (instead of $510,000) — $119,000 saved

The reason it’s so disproportionate: every dollar of extra principal in month 1 saves you the future interest on that dollar for 359 more months. The earlier the extra payment, the bigger the saving. Round numbers: an extra payment in year 1 saves you roughly the full nominal interest at the loan rate compounded for the remaining 29 years.

This is why “biweekly mortgage payment” services exist — they’re selling you a $0/month extra-principal program (one extra monthly payment per year, because there are 26 biweekly periods) repackaged as a “savings plan.” You can do the same thing for free by setting up an automatic transfer.

Rate matters more than you think

Same $400,000 loan, 30 years, three different rates:

A 1.5-point swing in rate is roughly $400/month and $137,000 in total interest. If you’re choosing between two lenders quoting rates 0.25 points apart, that’s about $66/month or $24,000 over the life of the loan.

This is why refinancing — even with closing costs — can pay back quickly when rates drop. Rough rule: divide your closing costs by the monthly savings; that’s your break-even in months. Anything under 24 months is usually worth doing.

What’s not in the PMT formula

The PMT formula gives you P&I — principal and interest. The “monthly payment” your lender will quote is usually PITI:

• Principal & Interest (the formula)
• Taxes — property tax, divided by 12. Often escrowed: the lender collects 1/12 of the annual tax each month and pays it for you.
• Insurance — homeowners insurance, also typically escrowed. Plus PMI (private mortgage insurance) if your down payment is <20%.
• HOA fees, if applicable. Not part of the loan but you’ll write the same check anyway.

On a $500K house with average tax (1.2%) and insurance ($1,500/yr), expect roughly:

P&I:        $2,528
Tax:          $500  (1.2% of $500K, /12)
Insurance:    $125
HOA:          $0–400 typical
TOTAL:      $3,153–3,553

That’s the number that has to fit in your budget — not just the $2,528 from the formula.

TL;DR

• One formula computes the P&I payment: M = P · r(1+r)^n / ((1+r)^n − 1).
• Early payments are mostly interest; this flips around the midpoint of the loan.
• Extra principal early is enormously valuable — every dollar avoids decades of compound interest.
• Rate matters a lot more than people expect. A 0.5-point difference is tens of thousands over the life of a loan.
• The lender’s “monthly payment” includes tax + insurance + maybe HOA. The PMT formula is just one of those four components.

Plug your own numbers into the mortgage calculator — the URL becomes a shareable, bookmarkable record of the scenario.