The formula
Payment = P × r ÷ (1 − (1 + r)−n)
- P is the amount you borrow (the principal).
- r is the interest rate per payment. For monthly payments it's the yearly rate ÷ 12, as a decimal: 6% a year is 0.06 ÷ 12 = 0.005.
- n is the number of payments: 30 years × 12 = 360.
Worked example: $200,000 at 6% for 30 years
- r = 0.06 ÷ 12 = 0.005, and n = 360.
- (1.005)360 ≈ 6.022575, so (1.005)−360 ≈ 0.166042.
- 1 − 0.166042 = 0.833958.
- 200,000 × 0.005 = 1,000, and 1,000 ÷ 0.833958 ≈ $1,199.10 a month.
Over 360 payments that's about $431,676 in total, so the interest is about $231,676.
Where each payment goes
Each month, interest is charged on what you still owe, and the rest of the payment reduces the balance. Early on you owe the most, so most of the payment is interest.
| Payment | Interest | Principal | Balance after |
|---|---|---|---|
| 1 | $1,000.00 | $199.10 | $199,800.90 |
| 2 | $999.00 | $200.10 | $199,600.80 |
| 3 | $998.00 | $201.10 | $199,399.70 |
The interest in month 1 is just $200,000 × 0.005 = $1,000. By the last years of the loan the split has flipped, and almost all of each payment goes to principal. Paying a little extra early cuts the total interest by far more than the extra you pay.
What the formula leaves out
A mortgage payment you actually send usually also includes property tax, home insurance and sometimes mortgage insurance (PMI) or HOA dues. The formula above is principal and interest only. Lenders may also round slightly differently, so your statement can differ by a few cents.
Do it with your numbers
The loan calculator and mortgage calculator do this instantly, the amortization calculator shows every payment's split, and the financial calculator solves for any of the five values (N, I/Y, PV, PMT, FV) like a business calculator.
Every worked example on this page was checked with Calcist's own engine and an independent reference.