How is a mortgage or loan payment calculated?
A loan payment comes from one formula with an exponent in it: M = Pi / (1 − (1 + i)⁻ⁿ). The exponent counts how many months interest has to build on the balance. Early payments go mostly to interest and later ones mostly to the loan, so paying a little extra early saves a lot.
- Monthly payment
- $255.74
- Total interest
- $2,721.93
- Total paid
- $17,721.93
- Interest saved by paying extra
- $691.00
Challenge: Save at least $10,000 in interest by paying extra each month.
More settings
Play
Drag the rate up by one point on a 30-year loan. Watch how much the interest block grows.
Challenge: Save at least $10,000 in interest by paying extra each month. The box under the picture turns green when you get it.
Stuck? Pick one of the examples from the “Try an example” menu, or press “New example.”
Understand
Each month the lender adds interest to what you still owe, then subtracts your payment. The payment is set so that after exactly months the balance lands on zero. Solving for that payment gives a formula with an exponent:
The term is how much a dollar paid months from now is worth today. It is compound interest run backwards, the same exponent as in savings.
The curve shows your balance. It falls slowly at first, because early payments mostly cover interest, then drops faster. The bar on the right splits everything you repay into the loan (blue) and interest (orange).
Use
Every input has a unit menu, so you can type values in the units you already have. Results follow your units.
Show the work
- Monthly rate and number of payments
i = \frac{r}{12} = 0.005833,\quad n = 12t = 72 - Payment formula
M = \frac{P\,i}{1 - (1 + i)^{-n}} - With your numbers
M = \frac{15{,}000\cdot\frac{0.07}{12}}{1 - \left(1 + \frac{0.07}{12}\right)^{-72}} - Result
M = \$255.74 - Interest with no extra payment
72 \times \$255.74 - \$15{,}000 \approx \$3{,}412.93 - Total interest, paying $50 extra each month
\$2{,}721.93\ \text{(paid off in 58 months)} - Interest saved
\$3{,}412.93 - \$2{,}721.93 = \$691.00
Compare loan lengths: $15,000 at 7%
| Length | Monthly payment | Total interest | Total paid |
|---|---|---|---|
| 10 years | $174.16 | $5,900 | $20,900 |
| 15 years | $134.82 | $9,268 | $24,268 |
| 20 years | $116.29 | $12,911 | $27,911 |
| 25 years | $106.02 | $16,805 | $31,805 |
| 30 years | $99.80 | $20,926 | $35,926 |
Same amount and rate for every row, with no extra payments. In real life a 15-year loan usually gets a slightly lower rate than a 30-year one, which widens the gap.
Year-by-year schedule (paid off in 4 years 10 months)
| Year | You pay | To interest | To the loan | Still owed |
|---|---|---|---|---|
| 1 | $3,669 | $964 | $2,704 | $12,296 |
| 2 | $3,669 | $769 | $2,900 | $9,395 |
| 3 | $3,669 | $559 | $3,110 | $6,286 |
| 4 | $3,669 | $334 | $3,334 | $2,951 |
| 5 | $3,047 | $95 | $2,951 | $0 |
Includes your extra $50.00 a month. Watch the “To the loan” column grow each year as the balance shrinks.
Export
Enter the amount, the APR, and the length. Open "More settings" to add an extra monthly payment and see the new payoff date and the interest saved.
- This is principal and interest only. Mortgage payments usually include property tax and insurance too.
- It assumes a fixed rate. Adjustable-rate loans change the payment when the rate resets.
- Lenders round to the cent each month, so their schedule can differ from this one by a few dollars.
For learning and estimation. Verify with applicable codes, standards, and a qualified professional before using in design, construction, or safety-critical work.
A real decision
Say you’re borrowing $750,000. In early November 2026, Freddie Mac’s weekly survey put the average 30-year fixed rate at 7.18% and the 15-year at 6.57%. Three ways to pay it:
| Plan | Per month | Paid off | Interest |
|---|---|---|---|
| 30 years, 7.18% | $5,080.76 | 30 yr | $1,079,074 |
| 30 years + $500 extra | $5,580.76 | 22 yr 10 mo | $775,027 |
| 15 years, 6.57% | $6,562.20 | 15 yr | $431,196 |
On the plain 30-year loan you pay back more in interest than you borrowed. In the first year, $53,611 of your $60,969 in payments goes to interest and only $7,358 goes to the loan.
The 15-year loan costs about $1,480 more a month and saves $647,878 in interest. The middle plan saves $304,047, and you can skip the extra $500 in a tight month, which a 15-year loan won’t let you do.
A rule of thumb many people use: if the 15-year payment fits your budget with room to spare, it is by far the cheapest way to own the house. If it would squeeze you, a 30-year loan with voluntary extra payments gets a big share of the savings and keeps your options open. Check that your loan has no prepayment penalty first. This is math, not financial advice.
Try it: set the exhibit to $750,000 at 7.18% and open Compare loan lengths in the Use tab.
Where people get stuck
- Using the yearly rate as the monthly rate. 7.18% a year is 0.5983% a month, so . Plug in 0.0718 by mistake and the $750,000 loan comes out to about $53,850 a month instead of $5,080.76.
- Counting years instead of months. The exponent is the number of payments: 30 years is . Using gives about $27,385 a month.
- Typing 7.18 instead of 0.0718. The formula needs the rate as a decimal. As a whole number it turns the payment into about $448,750 a month.
- Guessing interest as rate × amount × years. That gives $750,000 × 0.0718 × 30 = $1,615,500, half again too much. Interest is charged only on what you still owe, and that shrinks every month.
- Comparing payments but not totals. The 15-year payment looks much bigger, but the total interest is less than half. The Total interest column is the one that shows what the loan costs.
Cheat card
| Symbol | Meaning | Unit |
|---|---|---|
| monthly payment | $ | |
| amount borrowed | $ | |
| yearly rate as a decimal (APR) | ||
| monthly rate | ||
| number of monthly payments |
- A 15-year loan has a higher payment but often less than half the total interest of a 30-year loan.
- Extra payments go straight to the balance, so they skip all the interest that balance would have grown.
- Taxes, insurance, and HOA fees are not in this formula. Lenders add them on top of a mortgage payment.
Where it’s used
- Finance & Business
Every fixed-rate mortgage, car loan, and student loan payment in the US comes from this formula. Lenders’ amortization schedules are this same month-by-month loop. - Money & Shopping
Decide between a 15-year and a 30-year mortgage, or whether an extra $200 or $500 a month is worth it, before you ever talk to a lender. - Home Projects
Turn a listing price into a monthly number: subtract your down payment, enter today’s rate, then add property tax and insurance on top.
Related exhibits
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Go furtherCredit card payoff: how many months until it’s gone?
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Also tryPhone plans: finding the break-even point
Two plans, two lines. Where they cross, the price is the same.
Questions people ask
How do you calculate a monthly mortgage payment?
Divide the yearly rate by 12 to get the monthly rate i, and multiply the years by 12 to get n payments. Then M = Pi / (1 − (1 + i)⁻ⁿ). At 6% for 30 years, $200,000 costs $1,199.10 a month.
Why is so much of my early payment interest?
Interest is charged on the balance you still owe. At the start the balance is biggest, so most of the payment covers interest. As the balance shrinks, more of each payment goes to the loan itself.
Is it worth paying extra on a mortgage?
Extra payments cut the balance right away, so that money stops growing interest. On $300,000 at 6.5% for 30 years, $200 extra a month pays it off years early and saves tens of thousands in interest. Check first that your loan has no prepayment penalty.
What is APR?
The annual percentage rate, the yearly cost of borrowing. For a fixed-rate loan, divide it by 12 for the monthly rate. Official APR figures also fold in some fees, so they can be a little higher than the note rate.
Sources
- Freddie Mac Primary Mortgage Market Survey (weekly average rates) · checked November 8, 2026
- Freddie Mac news release: Mortgage Rates Decline for Third Consecutive Week to 7.18% (November 5, 2026) · checked November 8, 2026
Updated : New in the Use tab: compare loan lengths side by side, and a year-by-year amortization schedule. New worked case: a $750,000 loan at November 2026 average rates, 15 vs. 30 years and paying extra, with sources. New section on the most common mistakes, each with the wrong answer it gives.
Change history (5 revisions)
- · rev 5: New in the Use tab: compare loan lengths side by side, and a year-by-year amortization schedule. New worked case: a $750,000 loan at November 2026 average rates, 15 vs. 30 years and paying extra, with sources. New section on the most common mistakes, each with the wrong answer it gives.
- · rev 4: Fix "Show the work": with an extra monthly payment, the total-interest step showed interest without the extra payment, which didn't match the result. Now shows both, plus interest saved.
- · rev 3: Raise the loan amount slider maximum from $1,000,000 to $2,000,000.
- · rev 2: Note that mortgage payments usually add tax and insurance.
- · rev 1: First published.