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How to Calculate a Mortgage Payment (And What the Math Actually Does)
A mortgage payment looks mysterious until you see the formula that produces it. One equation, three inputs, and the same $1,896.20 your bank is quoting you pops out. Here's the math worked all the way through, plus the part the lender doesn't put on the rate sheet — why your early payments barely dent the balance, and why the number on your monthly statement is bigger than what the formula predicts.
Try the calculator → /mortgage.html — full PITI with PMI, taxes, insurance, and a month-by-month amortization schedule.
Last updated: May 4, 2026.
The formula, unpacked
Every fixed-rate mortgage payment in the country comes from this one equation:
PMT = P × [r(1+r)n] / [(1+r)n − 1]
Three inputs, nothing else:
- P — the loan principal (what you borrowed, not the home price).
- r — the monthly interest rate. Take the quoted annual rate and divide by 12. A 6.5% APR becomes
0.065 / 12 = 0.00541667. - n — the total number of monthly payments. A 30-year mortgage is
30 × 12 = 360.
The formula is designed to spit out exactly the fixed payment that will drive the balance to zero on month n. It's not magic — it's the algebraic solution to "what constant payment, applied every month, pays off a loan with compounding interest in exactly this many months?"
A real example: $300,000 at 6.5% for 30 years
Plug in the numbers. P = 300,000. r = 0.00541667. n = 360.
First compute (1 + r)n:
(1.00541667)360 ≈ 7.0298
Then the numerator: 0.00541667 × 7.0298 ≈ 0.038078
And the denominator: 7.0298 − 1 = 6.0298
Divide: 0.038078 / 6.0298 ≈ 0.006316
Multiply by principal: 300,000 × 0.006316 ≈ $1,896.20
That's the principal-and-interest payment your lender quotes. Multiply $1,896.20 by 360 payments and you get about $682,630 total — meaning you hand over roughly $382,630 in interest on top of the original $300,000 you borrowed. A house bought with a 30-year mortgage costs a bit more than twice its sticker price.
What "amortization" actually means
Your payment is fixed at $1,896.20 every month, but the split between interest and principal changes every single month. Interest is charged on whatever balance is still outstanding. In month 1, you owe the full $300,000, so the interest charge is:
300,000 × 0.00541667 = $1,625.00
That leaves only $1,896.20 − $1,625.00 = $271.20 to actually pay down the loan. In month 2 you owe $299,728.80, so the interest is a hair smaller and the principal chunk is a hair bigger. Repeat 358 more times and the balance lands at zero. That slow crossover is what amortization means.
Here's the split at three points on a $300,000, 6.5%, 30-year loan:
- Month 1 — payment $1,896.20 = $1,625.00 interest + $271.20 principal. Balance after: $299,728.80.
- Month 180 (halfway) — payment $1,896.20 ≈ $1,169 interest + $727 principal. Balance remaining: about $215,800. You've made half the payments but still owe 72% of the loan.
- Month 360 (final) — payment $1,896.20 ≈ $10 interest + $1,886 principal. Balance after: $0.
Notice how lopsided this is. At the halfway point in time, you've paid off less than a third of the principal. That is not a bank scam — it's just what the math does when interest is charged on the remaining balance and the payment is held constant.
Why one extra payment a year shaves 4–5 years off
Because early-loan payments are mostly interest, any extra dollar you throw at the principal in year 1 kills off a huge chain of future interest charges. One extra $1,896.20 payment per year on the example loan — easiest way is to add $158/month, which is 1/12 of a payment — pays the loan off in roughly 25.5 years instead of 30. That saves about $65,000 in interest.
Some people do this with a biweekly schedule: pay half your mortgage every two weeks. Because there are 26 biweekly periods in a year, you end up making 13 full monthly payments instead of 12 — the same "one extra payment" effect, just hidden in the cadence. The math doesn't care how you get the extra money in; it cares that principal drops faster early, which compounds savings over the remaining term.
Solving it on a financial calculator (TVM keys)
Nobody computes (1.00541667)360 by hand in the real world. The time-value-of-money keys on a financial calculator are built for exactly this. For the $300,000 at 6.5% for 30 years:
- P/Y = 12 (payments per year)
- N = 360
- I/Y = 6.5
- PV = 300,000 (money coming in to you from the bank)
- FV = 0 (you want the loan paid off at the end)
- Solve for PMT → −$1,896.20 (negative because it's going out of your pocket)
Try it on the financial calculator — the same TVM solver also handles "how much house can I afford" (solve for PV given a target PMT) and "what rate do I need?" (solve for I/Y given the other four).
The thing most people get wrong: P&I vs. PITI
The PMT formula gives you principal and interest. That's it. But the check your bank actually cashes every month usually includes two more line items: property taxes and homeowners insurance. If your down payment was less than 20%, it also includes private mortgage insurance (PMI). The industry shorthand for the whole stack is PITI — Principal, Interest, Taxes, Insurance.
Rough numbers for the $300,000 loan example, in a median-cost US market:
- Principal + Interest: $1,896
- Property taxes (1.2% of home value, escrowed monthly): ~$375
- Homeowners insurance (~$1,800/yr): ~$150
- PMI if down payment < 20% (~0.5% of loan): ~$125
- True PITI: roughly $2,420–$2,550
That's 25–30% higher than the P&I figure everyone quotes. When a lender "pre-approves you for $400,000," they're often looking at P&I against your income, not PITI. Budget for the full number, not the stripped-down one. HOA dues, if any, are on top of that.
Frequently asked questions
What if my mortgage is adjustable-rate (ARM) instead of fixed?
The same formula applies, but only for the current rate period. A 5/1 ARM uses the PMT formula with the initial rate for the first 60 months, then re-amortizes whatever balance is left at the new rate for the remaining 300 months. Every rate reset recalculates a new fixed PMT for the next period.
Is it always better to take a 15-year mortgage instead of a 30-year?
Financially yes, cash-flow-wise not always. A 15-year at 6% on $300,000 runs about $2,532/month — $636 more than the 30-year at 6.5%. You save roughly $220,000 in total interest, but you also commit to the higher payment with no flexibility. Many people take the 30-year and voluntarily pay extra, which gives most of the interest savings with the option to drop back to the minimum if money gets tight.
Does making extra principal payments lower my monthly payment?
No — it shortens the loan instead. The PMT is locked in at origination. Unless you formally "recast" the mortgage (some lenders offer this for a fee), extra principal payments just get you to the zero balance faster. If you want a lower monthly payment, you have to refinance or recast.
Why do the last few payments have almost no interest?
Because there's almost no balance left to charge interest on. By month 358 of a 30-year, you owe about $5,600. The interest on that at 6.5%/12 is about $30. Nearly the entire $1,896 payment goes to wiping out principal. That's the mirror image of month 1, where almost nothing did.
Try it yourself
Punch your own numbers — loan amount, rate, term — into the financial calculator and watch the PMT pop out. Then try adding an extra $100/month to the principal and see how many months you lop off. The leverage that compounding gives a homeowner who pays a little extra early is the same leverage that, in reverse, makes a 30-year mortgage cost double the sticker price of the house.
This article is for general education and is not financial advice. See our Terms.