The mortgage payment formula
A fixed-rate mortgage payment is the level monthly amount that pays each month's interest and retires the whole balance on the last payment. It depends on only three numbers: the loan amount, the monthly interest rate and the number of payments.
M = P × r × (1 + r)n ÷ ((1 + r)n − 1)M = monthly payment · P = loan amount · r = annual rate ÷ 12 (as a decimal) · n = years × 12
| Symbol | Meaning | Example |
|---|---|---|
| P | Amount borrowed (price − down payment) | $300,000 |
| r | Monthly rate = annual rate ÷ 100 ÷ 12 | 7.11 ÷ 1,200 = 0.005925 |
| n | Number of monthly payments = years × 12 | 30 × 12 = 360 |
| M | Monthly principal and interest | $2,018.12 |
Step-by-step example
Here is the calculation for $300,000 at 7.11%, the 30-year average in Freddie Mac's survey on Nov 12, 2026.[1] Carry at least six decimal places; rounding r early is the most common reason a hand calculation is off by a few dollars.
- Monthly rate. r = 7.11 ÷ 100 ÷ 12 = 0.005925.
- Number of payments. n = 30 × 12 = 360.
- Growth factor. (1 + r)n = 1.005925360 = 8.3872.
- Numerator. P × r × (1 + r)n = $300,000 × 0.005925 × 8.3872 = 14,908.23.
- Denominator. (1 + r)n − 1 = 7.3872.
- Payment. 14,908.23 ÷ 7.3872 = $2,018.12.
Over 360 payments you pay $726,523, of which $426,523 is interest. The calculator above shows every intermediate number for your own loan, and the mortgage payment calculator adds taxes, insurance and PMI to it.
Check the formula against an official example
You can test any calculator, including this one, against the CFPB's completed sample Loan Estimate: a $162,000 loan at 3.875% for 30 years shows monthly principal and interest of $761.78.[2] The formula gives $761.78: r = 0.00322917, n = 360.
How each payment splits into interest and principal
Each month's interest is the balance times r; the rest of the payment reduces the balance. Because the balance falls, interest falls and principal rises every month even though the payment stays the same.
Interest this month = balance × r$300,000 × 0.005925 = $1,777.50
| Payment | Starting balance | Interest | Principal | Ending balance |
|---|---|---|---|---|
| Month 1 | $300,000.00 | $1,777.50 | $240.62 | $299,759.38 |
| Month 2 | $299,759.38 | $1,776.07 | $242.04 | $299,517.34 |
| Month 3 | $299,517.34 | $1,774.64 | $243.48 | $299,273.86 |
In the first payment only $240.62 of $2,018.12 goes to principal. That is why extra payments made early save the most interest, and why a recast after a lump sum lowers the payment.
The formula in a spreadsheet
Spreadsheets have the formula built in. Rates and payments must use the same period, so divide the annual rate by 12:
| What you want | Formula | Result for this example |
|---|---|---|
| Monthly payment | =PMT(7.11%/12, 360, -300000) | $2,018.12 |
| Interest in month 1 | =IPMT(7.11%/12, 1, 360, -300000) | $1,777.50 |
| Principal in month 1 | =PPMT(7.11%/12, 1, 360, -300000) | $240.62 |
The minus sign before the loan amount makes the payment come out positive. The result is principal and interest only.
Rates, terms and the payment
The payment rises with the rate and falls with the term, but a longer term costs more interest in total:
| Rate | 15 years | 20 years | 30 years |
|---|---|---|---|
| 5.5% | $2,451 | $2,064 | $1,703 |
| 6% | $2,532 | $2,149 | $1,799 |
| 6.5% | $2,613 | $2,237 | $1,896 |
| 7% | $2,696 | $2,326 | $1,996 |
| 7.5% | $2,781 | $2,417 | $2,098 |
When the formula does not apply
The level-payment formula assumes a fixed rate and equal monthly payments. Other loans are calculated differently:
- Interest-only periods charge only balance × r until amortization starts; see the interest-only mortgage calculator.
- Adjustable-rate loans re-run the formula on the remaining balance and term each time the rate resets.
- HELOCs are open-end credit: the balance changes as you draw and repay,[3] and the draw period is commonly interest-only with principal optional.[4] The HELOC payment calculator handles both phases.
Principal and interest is not the whole paymentLenders usually collect property tax and insurance with the payment, and PMI if you put down less than 20%. Use the home mortgage calculator for the full monthly cost of owning.
Frequently asked questions
What is the formula for a monthly mortgage payment?
M = P × r × (1 + r)n ÷ ((1 + r)n − 1), where P is the loan amount, r is the annual rate divided by 12 and n is the number of monthly payments.
How do you calculate the interest on a mortgage payment?
Multiply the balance owed by the monthly rate. On $300,000 at 7.11%, the first month's interest is $1,777.50; the rest of the payment reduces the balance.
How do I calculate my mortgage payment in Excel?
Use =PMT(rate/12, years*12, -loan). For this example: =PMT(7.11%/12, 360, -300000) returns $2,018.12.
Why is my lender's payment different from my calculation?
Usually because the lender's figure includes taxes, insurance and mortgage insurance, or because the rate or loan amount you used differs slightly (for example, points or a financed fee). Principal and interest alone should match the formula to the cent.