The Monthly Payment Formula: Variables, Amortization and Examples
Use the fixed-rate amortization formula, define every variable, and verify loan examples generated by the same shared finance functions as the calculators.
This is the mathematical reference for a standard fully amortizing fixed-rate loan. It explains the formula and amortization mechanics; it does not estimate taxes, insurance, lender fees, or loan eligibility.
The monthly payment formula
M = P × [r(1+r)^n] / [(1+r)^n − 1]
- M is the level monthly principal-and-interest payment.
- P is the starting loan principal.
- r is the nominal annual rate divided by 12 and expressed as a decimal.
- n is the number of scheduled monthly payments.
The formula assumes equal end-of-month payments and a fixed rate for the modeled term. A note rate is distinct from APR when fees or other charges are included.
Three examples from the shared calculation
- A $10,000 loan at 10% for 3 years produces $322.67 per month and $1,616.19 of total interest.
- A $25,000 loan at 7% for 5 years produces $495.03 per month and $4,701.80 of total interest.
- A $300,000 loan at 6.8% for 30 years produces $1,955.78 per month and $404,079.20 of total interest.
Why early payments contain more interest
Interest is calculated on the outstanding balance. In the first month of the $300,000 example, interest is $1,700.00 and principal is $255.78. The payment remains $1,955.78, but the interest share falls as the balance declines.
Rate and term sensitivity
| Rate | Years | Monthly payment | Total interest | Total paid |
|---|---|---|---|---|
| 5.5% | 15 | $2,451.25 | $141,225.07 | $441,225.07 |
| 5.5% | 30 | $1,703.37 | $313,212.12 | $613,212.12 |
| 6.8% | 15 | $2,663.05 | $179,349.31 | $479,349.31 |
| 6.8% | 30 | $1,955.78 | $404,079.20 | $704,079.20 |
| 7.5% | 15 | $2,781.04 | $200,586.67 | $500,586.67 |
| 7.5% | 30 | $2,097.64 | $455,151.67 | $755,151.67 |
Use the monthly payment calculator to check another input set or the amortization schedule to inspect every payment. For property taxes, insurance, and other housing-cost inputs, continue to the mortgage payment guide.