The Mortgage Payment Formula
Every fixed-rate mortgage payment comes from one formula, the standard loan amortization formula:
M = P × r(1 + r)n / [(1 + r)n − 1]
- M = monthly payment of principal and interest
- P = loan amount (the home price minus your down payment)
- r = monthly interest rate: the annual rate as a decimal, divided by 12
- n = number of monthly payments: years × 12 (360 for a 30-year loan)
The formula finds the one payment that, made every month, covers that month's interest and pays the balance down to exactly zero on the last payment. Taxes, insurance and PMI are added on top; we cover them below.
Step-by-Step Example: $320,000 at 7% for 30 Years
Say you buy a $400,000 home with 20% down, borrowing $320,000 at 7.00% on a 30-year fixed mortgage.
1. Monthly rate: r = 0.07 ÷ 12 = 0.0058333
2. Number of payments: n = 30 × 12 = 360
3. Growth factor: (1 + r)n = (1.0058333)360 = 8.1165
4. Numerator: P × r × 8.1165 = 320,000 × 0.0058333 × 8.1165 = 15,150.80
5. Denominator: 8.1165 − 1 = 7.1165
6. Payment: M = 15,150.80 ÷ 7.1165 = $2,128.97
Over 360 payments you pay $766,428 in total: the $320,000 you borrowed plus $446,428 in interest. Keep at least six decimal places for r; rounding it early is the usual reason a hand calculation is off by a few dollars.
For reference, the average 30-year fixed rate was 7.24% on October 29, 2026 in Freddie Mac's weekly survey.
How Each Payment Splits Between Interest and Principal
Interest each month is the current balance times r. In month one that is 320,000 × 0.0058333 = $1,866.67, so only $262.30 of the $2,128.97 payment reduces the balance. As the balance falls, the interest share shrinks and the principal share grows:
| Payment | Amount | Interest | Principal | Balance |
|---|---|---|---|---|
| 1 | $2,128.97 | $1,866.67 | $262.30 | $319,737.70 |
| 2 | $2,128.97 | $1,865.14 | $263.83 | $319,473.87 |
| 3 | $2,128.97 | $1,863.60 | $265.37 | $319,208.50 |
With this loan, principal does not overtake interest until payment 242, about 20.2 years in. Where the loan stands at milestones:
| After year | Balance left | Principal repaid | Interest paid |
|---|---|---|---|
| 1 | $316,749 | $3,251 | $22,297 |
| 5 | $301,221 | $18,779 | $108,959 |
| 10 | $274,600 | $45,400 | $210,076 |
| 15 | $236,860 | $83,140 | $300,075 |
| 20 | $183,360 | $136,640 | $374,313 |
| 25 | $107,517 | $212,483 | $426,208 |
| 30 | $0 | $320,000 | $446,428 |
You can find the balance after any number of payments k without building the full schedule:
Balance = P(1 + r)k − M × [(1 + r)k − 1] / r
After five years (k = 60) the balance is $301,221.09. Our mortgage payment calculator prints the complete month-by-month amortization schedule.
Try It With Your Numbers
The calculator below runs the same formula. It is preset to the example: a $400,000 home, $80,000 down, 7% for 30 years.
From Principal and Interest to Your Full Payment (PITI)
The formula gives principal and interest only. Lenders qualify you on PITI: principal, interest, taxes and insurance, plus mortgage insurance and HOA dues where they apply:
| Cost | How to estimate it | Example |
|---|---|---|
| Principal and interest | The formula above | $2,128.97 |
| Property tax | Home value × local tax rate ÷ 12 (1.1% here) | $366.67 |
| Homeowners insurance | Annual premium ÷ 12 ($1,800 a year here) | $150.00 |
| PMI | Usually 0.3% to 1.5% of the loan a year with less than 20% down | $0 (20% down) |
| Total | $2,645.63 |
Most lenders want this total to stay under about 28% of your gross monthly income, and all your debt payments under about 36%. The home affordability calculator works backward from your income, and our affordability by state report shows the income needed for the median home in every state.
15-Year vs. 30-Year: The Formula Side by Side
A shorter term means fewer payments (n = 180) and usually a lower rate, so the payment rises but the total interest falls sharply. The same $320,000 loan, using example rates:
| 30-year at 7.00% | 15-year at 6.25% | |
|---|---|---|
| Monthly payment | $2,128.97 | $2,743.75 |
| Total interest | $446,428 | $173,876 |
| Total paid | $766,428 | $493,876 |
The 15-year loan costs $615 more a month and saves $272,553 in interest. Compare any two loans with the mortgage comparison calculator.
Monthly Payment per $100,000 Borrowed
Because the payment is proportional to the loan amount, a per-$100,000 table lets you size any loan: multiply by the loan amount in hundreds of thousands. A $250,000 loan at 6.5% for 30 years costs 2.5 times the 6.50% row.
| Rate | 30-year payment | 15-year payment | 30-year total interest |
|---|---|---|---|
| 5.00% | $536.82 | $790.79 | $93,256 |
| 5.50% | $567.79 | $817.08 | $104,404 |
| 6.00% | $599.55 | $843.86 | $115,838 |
| 6.50% | $632.07 | $871.11 | $127,544 |
| 7.00% | $665.30 | $898.83 | $139,509 |
| 7.50% | $699.21 | $927.01 | $151,717 |
| 8.00% | $733.76 | $955.65 | $164,155 |
Each half-point of rate adds roughly $31 to $35 a month per $100,000 on a 30-year loan, which is why shopping lenders for a slightly lower rate pays off.
Extra Payments: How Many Months Do You Save?
To find how long a loan takes to pay off at a given payment, solve the formula for n:
n = −ln(1 − r × P / M) / ln(1 + r)
Adding $200 a month to the example payment ($2,328.97 instead of $2,128.97) gives n = 278.00: the loan is paid off with 278 full payments and a small final one, instead of 360 payments. That is about 6.8 years sooner, and you save roughly $118,972 in interest. The “How Fast Can I Pay Off?” tab of the calculator above runs this for any payment.
Mortgage Formulas in Excel and Google Sheets
Spreadsheets have the amortization formula built in. Enter the loan as a negative present value to get positive results:
| What you want | Formula | Result |
|---|---|---|
| Monthly payment | =PMT(0.07/12, 360, -320000) | $2,128.97 |
| Interest in payment 1 | =IPMT(0.07/12, 1, 360, -320000) | $1,866.67 |
| Principal in payment 1 | =PPMT(0.07/12, 1, 360, -320000) | $262.30 |
| Balance after 60 payments | =FV(0.07/12, 60, 2128.97, -320000) | $301,221.09 |
| Total interest over the loan | =-CUMIPMT(0.07/12, 360, 320000, 1, 360, 0) | $446,428.47 |
| Months to pay off with $200 extra | =NPER(0.07/12, -2328.97, 320000) | 278.00 |
Common Mistakes When Calculating a Mortgage Payment
- Using the annual rate. r must be the monthly rate. Plugging in 0.07 instead of 0.07/12 gives a wildly wrong payment.
- Using years for n. A 30-year loan has 360 payments, not 30.
- Using the APR. The payment is based on the note rate. The APR is usually higher because it spreads fees and points over the loan, so it is a tool for comparing offers, not for computing the payment.
- Forgetting the rest of PITI. Taxes and insurance often add 20% to 40% to the principal and interest payment.
- Rounding too early. Keep r to at least six decimal places until the final step.