How Mortgage Payments Are Calculated
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Your principal-and-interest payment is calculated with the standard loan amortization formula: M = P x [r(1+r)^n] / [(1+r)^n - 1]. For a $400,000 loan at 6.5% over 30 years, that works out to about $2,528 a month before taxes, insurance or PMI are added.
A fixed-rate mortgage payment is not a guess — it comes from one algebraic formula applied to your loan amount, rate and term. Understanding that formula explains why a small rate change moves your payment so much, and why early payments are almost all interest.
Key takeaways
- Principal and interest come from one fixed formula; taxes, insurance and PMI are added separately.
- Early payments are mostly interest because interest is charged on the remaining balance, which starts at its highest point.
- A 1-point rate difference on a $400,000, 30-year loan changes the payment by roughly $250-$270 a month.
- A calculator estimate is a planning number; your official cost comes from a lender's Loan Estimate.
Run the numbers with the Mortgage Calculator.
The amortization formula
M = P x [ r(1+r)^n ] / [ (1+r)^n - 1 ], where P is the loan principal, r is the monthly interest rate (annual rate divided by 12) and n is the total number of monthly payments.
The formula solves for the single constant payment that reduces the balance to exactly zero after n payments. When the interest rate is zero the formula is undefined algebraically, and the payment is simply P divided by n.
Worked example: $400,000 at 6.5% over 30 years
Start with P = $400,000, annual rate 6.5%, so r = 0.065 / 12 = 0.0054167, and n = 30 x 12 = 360 monthly payments.
- Calculate (1+r)^n: (1.0054167)^360 ≈ 7.0333.
- Multiply the numerator: r(1+r)^n = 0.0054167 x 7.0333 ≈ 0.038096.
- Calculate the denominator: (1+r)^n - 1 = 7.0333 - 1 = 6.0333.
- Divide: 0.038096 / 6.0333 ≈ 0.0063139.
- Multiply by principal: M = 400,000 x 0.0063139 ≈ $2,525.60 per month.
Why early payments are mostly interest
Each month, interest is charged on the remaining balance: balance x r. Whatever is left of the fixed payment reduces the principal. Because the balance starts at its maximum, the interest share starts at its maximum too.
On the $400,000 example above, the first month's interest is 400,000 x 0.0054167 ≈ $2,166.68, out of a $2,525.60 payment — about 86% interest. By year 20, most of the payment goes to principal. This is why extra principal paid early has a much larger lifetime effect than the same extra dollar paid late.
What else is in the monthly housing payment
- Principal and interest — the amortized loan payment from the formula above.
- Property tax — usually collected monthly into an escrow account and paid to the county on your behalf.
- Homeowners insurance — also commonly escrowed.
- Mortgage insurance (PMI) — typically required on conventional loans while the loan-to-value ratio exceeds 80%.
- HOA dues — paid directly to the association, not to your lender, but still part of your housing budget.
How rate changes the payment
Principal and interest on a $400,000, 30-year fixed loan at different rates
| Rate | Monthly P&I | Total interest paid |
|---|---|---|
| 5.5% | $2,271 | $417,560 |
| 6.0% | $2,398 | $463,353 |
| 6.5% | $2,528 | $510,127 |
| 7.0% | $2,661 | $557,838 |
Why a lender quote differs from a calculator
A calculator uses the rate you type in. A lender prices your specific loan using credit score, loan-to-value, occupancy, loan type, points paid, lock period and current market conditions. Escrow amounts also depend on the actual assessed tax bill and quoted insurance premium, not a rough estimate.
Treat calculator output as a planning figure, then compare official Loan Estimates from lenders before committing to one.
Common mistakes
- Comparing a calculator's principal-and-interest number to a lender's full PITI quote and assuming a discrepancy is an error.
- Ignoring PMI when the down payment is below 20% on a conventional loan.
- Using a national average property tax rate instead of the local rate for the actual county.
- Forgetting that an adjustable-rate loan's payment shown today is only accurate until the first rate reset.
Practical considerations
Two loans with the same rate and term but different points or fees are not identical in cost — compare the annual percentage rate (APR) alongside the note rate. A shorter term (15 years instead of 30) raises the monthly payment substantially but cuts total interest by more than half in most cases, because both r stays the same per period while n shrinks and the balance is repaid faster.
Second example: the same formula on a shorter term
The formula does not change shape for a different term — only n changes. Take a $600,000 loan at 6.0% over 15 years instead of 30.
- r = 0.06 / 12 = 0.005, and n = 15 x 12 = 180 payments.
- (1.005)^180 ≈ 2.4541.
- Numerator: 0.005 x 2.4541 ≈ 0.012271. Denominator: 2.4541 - 1 = 1.4541.
- Divide and multiply by principal: 600,000 x (0.012271 / 1.4541) ≈ $5,063 per month.
- Compare that with the same $600,000 at 6.0% over 30 years, which computes to roughly $3,597 per month — a $1,466 higher payment for the 15-year term.
- Total interest tells the other side of the story: the 15-year loan pays about $311,000 in interest over its life, versus about $695,000 for the 30-year loan at the same rate — less than half, even though the rate did not change.
How the interest/principal split moves over the life of a loan
Using the original $400,000, 6.5%, 30-year example, the table below shows the remaining balance and that month's interest-versus-principal split at several points in the schedule.
Amortization snapshot, $400,000 loan at 6.5% over 30 years
| Loan year | Remaining balance | Interest that month | Principal that month |
|---|---|---|---|
| Year 1 | $400,000 | $2,167 | $359 |
| Year 11 | $339,560 | $1,840 | $686 |
| Year 21 | $223,880 | $1,213 | $1,313 |
| Year 26 | $131,120 | $710 | $1,815 |
Frequently asked questions
Does the amortization formula include taxes and insurance?
No. The formula calculates only principal and interest. Taxes, homeowners insurance, mortgage insurance and HOA dues are added on top to get your total monthly housing payment, often called PITI.
Why does my payment stay the same but the interest portion change?
The total payment is fixed for the life of a fixed-rate loan, but each month interest is recalculated on the remaining balance. As the balance falls, the interest portion falls and the principal portion rises, even though the total payment does not change.
How much does an extra principal payment actually save?
Extra principal reduces the balance immediately, which lowers every future month's interest charge. Paid early in the loan, when the balance and interest share are highest, extra payments save more in total interest than the same amount paid later.
Is a 15-year loan always better than a 30-year loan?
It generally costs less in total interest and often carries a lower rate, but it comes with a materially higher required monthly payment. The right choice depends on your monthly budget and other financial priorities, not just total interest.
Does making biweekly payments really save money?
Splitting the monthly payment into two biweekly payments results in 26 half-payments a year, equal to 13 full monthly payments instead of 12 — one extra payment annually, applied to principal. That extra principal reduces the balance faster and cuts total interest, but the effect comes from the extra payment, not from any change to the underlying formula.
Why did my payment go up even though my rate is fixed?
The principal-and-interest portion calculated by the formula does not change on a fixed-rate loan. If your total payment rose, the most common cause is an escrow adjustment — your property tax or homeowners insurance bill increased, so the lender raised the monthly escrow contribution to cover it.
How is an adjustable-rate mortgage payment calculated differently?
An ARM uses the same amortization formula, but r and the remaining n are recalculated at each adjustment using the new index-based rate and the balance and time remaining at that point. The payment shown today is accurate only until the next scheduled adjustment.
Sources and references
- Consumer Financial Protection Bureau — Loan Estimate explainer — Line-by-line breakdown of the official payment and cost disclosure lenders must provide.
- Freddie Mac — Primary Mortgage Market Survey — Weekly national average fixed mortgage rates used for realistic rate assumptions.
- CFPB — What is amortization? — Plain-language definition of how each payment splits between interest and principal.