A mortgage payment looks like one number, but it is really four or five numbers added together, and only one of them is set by the famous formula. If you borrow $300,000 at 6.5% for 30 years, the loan itself costs $1,896.20 a month. By the time taxes, insurance, and possibly PMI are stacked on top, the real bill can pass $2,400. This guide walks through the whole calculation step by step, with the actual math, so you can check any lender’s quote yourself or test scenarios in our free mortgage calculator.
In this guide
- The mortgage payment formula
- A worked example, digit by digit
- PITI: what a real monthly payment contains
- 15 vs 30 years: what the term really costs
- How much one percentage point matters
- Down payment and PMI
- Extra payments: small money, big years
- How much house you can afford
- Run your own numbers
- Frequently asked questions
The mortgage payment formula
Almost every fixed-rate mortgage in the world uses the same amortization formula:
M = P × [ r(1 + r)n ] / [ (1 + r)n − 1 ]
Each symbol has a precise meaning:
- M is the monthly payment for principal and interest only.
- P is the loan amount (the home price minus your down payment).
- r is the monthly interest rate: the annual rate divided by 12. A 6.5% rate means r = 0.065 / 12 = 0.0054167.
- n is the total number of payments: years × 12. A 30-year loan means n = 360.
The formula is built so that the same fixed payment, made n times, pays off the entire balance plus all the interest that accrues along the way. Early payments are mostly interest, late payments are mostly principal, and the split shifts every single month. We cover that shift in detail in our guide to where your payment actually goes.
A worked example, digit by digit
Take a $300,000 loan at 6.5% for 30 years.
- Monthly rate: r = 0.065 / 12 = 0.0054167
- Number of payments: n = 30 × 12 = 360
- Growth factor: (1 + r)360 = (1.0054167)360 ≈ 7.0413
- Numerator: 0.0054167 × 7.0413 ≈ 0.038140
- Denominator: 7.0413 − 1 = 6.0413
- M = 300,000 × (0.038140 / 6.0413) = $1,896.20
Two more numbers fall straight out of this. Total paid over the life of the loan: 360 × $1,896.20 = $682,633. Total interest: $682,633 − $300,000 = $382,633. Yes, at 6.5% over 30 years you pay more in interest than you borrowed. That is not a trick, it is just what 360 months of compounding costs, and it is exactly why the term and rate sections below matter so much.
PITI: what a real monthly payment contains
Lenders and budgeting guides talk about PITI: Principal, Interest, Taxes, Insurance. The formula above covers only the first two. A realistic monthly bill for the same $300,000 loan might look like this:
| Item | Monthly | Where it comes from |
|---|---|---|
| Principal and interest | $1,896.20 | The amortization formula |
| Property tax | $360.00 | Roughly 1 to 1.5% of home value per year, set by your county |
| Homeowners insurance | $125.00 | Annual premium divided by 12 |
| PMI | $112.50 | Only if your down payment was under 20% |
| HOA fee | $0 to $400 | Only in associations and condos |
Taxes and insurance are usually collected into an escrow account, so they arrive bundled into one payment even though they have nothing to do with the loan math. When you compare offers, always separate the loan cost (principal and interest) from the carrying costs (the rest), because lenders only control the first one.
15 vs 30 years: what the term really costs
Shortening the term raises the monthly payment less than people expect and cuts the interest more than people expect, because every extra year is another year of interest on a still-large balance.
| 30-year at 6.5% | 15-year at 6.5% | |
|---|---|---|
| Monthly payment | $1,896.20 | $2,613.32 |
| Total paid | $682,633 | $470,398 |
| Total interest | $382,633 | $170,398 |
The 15-year loan costs $717 more per month and saves $212,235 in interest. In practice 15-year loans also carry lower rates than 30-year loans, which widens the gap further. If the higher payment feels risky, the extra-payments section below shows a middle path with no contractual obligation.
How much one percentage point matters
On the same $300,000 over 30 years:
| Rate | Monthly payment | Difference vs 6.5% |
|---|---|---|
| 5.5% | $1,703.37 | −$192.83 per month, −$69,419 over the loan |
| 6.5% | $1,896.20 | baseline |
| 7.5% | $2,097.64 | +$201.44 per month, +$72,518 over the loan |
A single percentage point moves the monthly payment by roughly $200 and the lifetime cost by roughly $70,000 at this loan size. This is why shopping two or three lenders, improving your credit score before applying, and considering points all have a measurable payoff. To see the effect at your own loan size, change only the rate field in the calculator and watch the total interest line.
Down payment and PMI
The down payment changes the calculation twice. First, it shrinks P, and every dollar removed from P saves about $1.27 over a 30-year 6.5% loan. Second, it decides whether you pay PMI, private mortgage insurance, which most conventional lenders require when the down payment is under 20%.
PMI typically costs 0.3% to 1.5% of the loan balance per year. On a $270,000 loan (10% down on a $300,000 home) at a 0.5% PMI rate, that is $112.50 a month. PMI is not forever: by law it must end once your balance falls to 78% of the original home value, and you can usually request cancellation at 80%. Still, on this example it adds over $1,300 a year while it lasts, money that buys you nothing but the loan itself.
Extra payments: small money, big years
Anything you pay above the required amount goes straight to principal, and principal you remove today stops generating interest for every remaining month. The effect compounds in your favor.
On the $300,000, 6.5%, 30-year example, paying just $200 extra each month:
- Pays the loan off in 277 months instead of 360, about 23.1 years, nearly 7 years early.
- Cuts total interest from $382,633 to $279,185, a saving of $103,449.
That is a better return than most savings accounts will ever give you, guaranteed and tax-free. If you carry several debts at different rates, run them through the debt payoff calculator first, because extra money usually belongs on the highest-rate debt, which is rarely the mortgage.
How much house you can afford
The classic lender screen is the 28/36 rule: housing costs (full PITI) should stay under 28% of gross monthly income, and all debt payments together under 36%. On an $85,000 salary, gross monthly income is $7,083, so the housing budget is about $1,983 and the all-debt ceiling about $2,550. Note that both limits use gross income, before tax, so the real bite out of take-home pay is larger than the percentages suggest. To translate an hourly wage or a net figure into gross annual income, use the salary calculator.
One more quiet enemy of affordability is inflation: a payment that feels heavy today will feel lighter in ten years as wages drift up, which is one genuine advantage of a fixed-rate loan. The inflation calculator shows what any amount will be worth down the road.
Run your own numbers
Every figure in this guide came from the same math you can run yourself, free and in the browser:
- Mortgage calculator: full PITI breakdown, charts, amortization schedule, extra payments.
- Loan calculator: the same amortization math for car, personal, or student loans.
- Debt payoff calculator: snowball vs avalanche across several debts.
- Compound interest calculator: the same compounding, working for you instead of against you. We unpack that side of the math in our compound interest guide.
- Investment calculator: solve for any missing variable in a savings plan.
- Retirement calculator: long-horizon planning with contributions.
Frequently asked questions
Why is my first payment almost all interest?
Interest is charged on the current balance, and at the start the balance is the whole loan. On $300,000 at 6.5%, the first month accrues $1,625 of interest, so only $271.20 of a $1,896.20 payment reduces the debt. The split improves every month as the balance falls.
Does paying extra change my required monthly payment?
No. On a fixed-rate mortgage the required payment stays the same; extra payments shorten the loan instead. If you want a lower required payment you would need to refinance or recast the loan.
Is PMI the same as homeowners insurance?
No. Homeowners insurance protects you and the property. PMI protects the lender if you default, and you pay for it. It applies only while your equity is under the 20% threshold.
Are taxes and insurance part of the mortgage formula?
No. The formula covers principal and interest only. Taxes and insurance are added on top, usually through an escrow account, and they change over time even though your loan payment does not.
How accurate is the 28/36 rule?
It is a screening rule, not a law. Lenders may stretch it with strong credit, and your own budget may demand stricter limits. Treat 28/36 as the outer boundary, then build the real decision from your actual monthly cash flow.