How Mortgage Amortization Is Calculated

The Core Formula

Every fixed-rate mortgage payment is calculated with one formula:

M = P × [r(1+r)ⁿ] / [(1+r)ⁿ − 1]

• M — your fixed monthly principal & interest payment
• P — the loan principal (amount borrowed)
• r — your monthly interest rate (annual rate ÷ 12, as a decimal)
• n — total number of monthly payments (loan term in years × 12)

This formula gives you one number that stays fixed for the life of the loan. What changes every month is how that fixed payment splits between interest and principal — which is what "amortization" describes, and what the rest of this page walks through.

Step-by-Step: Calculating a Single Month

Once you have M, generating a schedule is four repeated steps for every month:

1. Multiply the current balance by r to get that month's interest charge.
2. Subtract that interest from M to get that month's principal payment.
3. Subtract the principal payment from the balance to get the new balance.
4. Repeat, using the new balance, for the next month.

Worked Example: $320,000 at 6.5%, 30 Years

P = $320,000, annual rate = 6.5% so r = 0.065 ÷ 12 = 0.0054167, n = 360.

Plugging into the formula: M = 320,000 × [0.0054167 × (1.0054167)³⁶⁰] / [(1.0054167)³⁶⁰ − 1] ≈ $2,022.62.

Now the first three months, calculated by hand:

Notice the interest is barely dropping and the principal barely rising, month to month, at this early stage — that's the front-loaded interest effect every 30-year loan has, and it only reverses gradually over the decades that follow.

Layering in PMI

Private mortgage insurance is calculated independently of principal and interest — it's typically an annual percentage of the original loan amount (commonly 0.3%-1.5%), divided by 12 for a monthly charge, and added on top of M. It continues until your loan-to-value ratio (current balance ÷ original home value) drops to the cancellation threshold — usually 80% — per the Homeowners Protection Act rules the CFPB enforces. Our calculators track your balance against your home value every month and drop PMI from the schedule automatically at that point.

Layering in Escrow (Taxes, Insurance, HOA)

Property taxes and homeowners insurance don't amortize the way principal and interest do — they're simply annual costs divided by 12 and added to your payment as escrow. HOA dues are usually paid directly to the association rather than escrowed by the lender, which is why we display it as a separate line rather than folding it into the escrow total.

How Extra Payments and Biweekly Schedules Change the Math

Any extra principal you pay in a given month is simply subtracted from the balance in addition to that month's scheduled principal — which means every subsequent month's interest (balance × r) is calculated on a smaller number, compounding the savings for the rest of the loan. A biweekly schedule (half your payment every two weeks = 26 half-payments = 13 full payments/year) is mathematically equivalent to adding one extra 1/12th-of-a-payment as additional principal every month, which is how we model it.

The Full 30-Year Schedule at a Glance

Continuing the same $320,000-at-6.5% example, here's what the same month-by-month process produces at four checkpoints across the full term — useful for sanity-checking your own numbers against a known reference:

Two things stand out. First, by year 10 — a third of the way through the loan — barely 15% of the principal has been repaid, even though a third of the payments have been made. Second, cumulative interest ($408,142) ends up larger than the entire amount borrowed ($320,000): on this example, borrowing the money costs more than the money itself, spread out over three decades. Neither number is unusual — it's simply what a 30-year amortization schedule looks like at this rate, and it's the same math underneath every one of our calculators, just with your own inputs instead of this example's.

The Math Behind Recast, Balloon, and Refinance Calculators

Three other calculators on this site reuse the same core formula above, just applied differently:

• Recast— takes your current balance, subtracts a lump-sum payment, then re-runs M = P × [r(1+r)ⁿ] / [(1+r)ⁿ − 1] using the new, smaller P, but keeps the same r (your existing rate) and the same n (your remaining term). The result is a lower monthly payment with the identical payoff date — nothing about the schedule's shape changes, it just restarts from a smaller balance. See the full walkthrough on our mortgage recast calculator.
• Balloon— computes M using a long n (say 360 months, for affordability), but only generates schedule rows up to an earlier balloon month. The "balloon payment due" is simply whatever balance remains at that earlier month — read directly off the same schedule table this page describes, just cut short. Full detail on our balloon mortgage amortization calculator.
• Refinance — runs the formula twice: once for your current loan (current balance, current rate, remaining months) and once for the proposed new loan (current balance plus closing costs, new rate, new term), then compares the two resulting M values and total-interest figures side by side. The break-even month is simply closing costs divided by the monthly savings between the two. Worked through in full on our refinance amortization calculator.

Amortization vs. Simple Interest

It's worth being precise about what "amortization" is not, since the term gets confused with simple interest in casual conversation. Simple interest charges a flat rate against the original principal for the life of a loan — the interest amount never changes, whether it's month 1 or month 300. Amortization recalculates interest every single period against whatever balance actually remains, which is why the interest charge in our worked example above shrinks from $1,733.33 in month 1 down toward single digits by the final months of the loan. Mortgages, auto loans, and most installment debt use amortization; a small number of specialty and short-term products use simple interest instead. If a lender ever quotes you a rate without specifying which method applies, ask directly — the two produce meaningfully different total-interest outcomes on the same nominal rate and term.

A related point of confusion: amortization is also used as an accounting term for spreading the cost of an intangible asset over time, which has nothing to do with loan repayment. On this site, "amortization" always refers to the loan-repayment meaning described above.

Rounding and Edge Cases

A handful of edge cases come up in any real amortization implementation, and it's worth knowing how we handle each:

• The final payment. Because M is calculated once and held fixed, tiny rounding differences can leave a few cents of balance after the scheduled final payment. Our calculator caps the last payment so the balance lands at exactly $0.00 rather than carrying a residual fraction of a cent forward.
• Extra payments that exceed the remaining balance.If an extra payment in a given month is larger than what's still owed, we cap the principal paid at the remaining balance rather than showing a negative number — the loan simply ends that month.
• Zero-percent financing.When r = 0, the standard formula divides by zero. We detect this case separately and use the simpler M = P ÷ n instead, which is the correct payment for an interest-free loan.
• Adjustable-rate mortgages (ARMs). Every calculator on this site assumes a fixed rate for the full term. An ARM technically runs this same formula fresh at each reset — recalculating M using the new rate and whatever months remain — rather than a single fixed calculation for the whole loan. To model an ARM reset yourself, run the numbers here twice: once for the initial fixed period, then again using your remaining balance, the new rate, and your remaining term.

Data Sources We Cite

For current mortgage rate context, we reference Freddie Mac's Primary Mortgage Market Survey, published weekly since 1971. For PMI cancellation rules, we reference the Consumer Financial Protection Bureau, which enforces the Homeowners Protection Act. We link directly to primary sources rather than summarizing secondhand.

How This Page Was Produced

This methodology was drafted with AI research assistance and independently verified by Sukie Gao — every formula and worked example on this page was checked against a hand calculation before publishing. See our About page for more on our editorial process.