The standard amortization payment formula
- M
- regular payment
- P
- principal or original loan balance
- r
- interest rate per payment period
- n
- total number of payments
For monthly payments, divide the nominal annual rate by 12 to obtain the monthly periodic rate. Multiply the term in years by 12 to obtain the number of payments.
Example: $200,000 at 6% for 30 years
- Principal: $200,000
- Annual rate: 6.00%
- Monthly rate: 0.06 ÷ 12 = 0.005
- Number of payments: 30 × 12 = 360
- Calculated monthly payment: $1,199.10
The payment remains fixed, but the interest and principal portions change as the balance declines.
First three rows of the schedule
| Payment | Payment amount | Interest | Principal | Balance |
|---|---|---|---|---|
| 1 | $1,199.10 | $1,000.00 | $199.10 | $199,800.90 |
| 2 | $1,199.10 | $999.00 | $200.10 | $199,600.80 |
| 3 | $1,199.10 | $998.00 | $201.10 | $199,399.70 |
Each row uses the prior row's ending balance. Interest equals the starting balance multiplied by 0.005. Principal equals the payment minus interest.
Why software and spreadsheets can differ by a few cents
Programs may round interest to cents on every row or retain additional precision until totals are displayed. Exact dates and day-count conventions can also produce a different result than a simple monthly periodic formula.
When comparing a lender statement, use the same dates, compounding assumptions, rounding rules, and payment-posting method.
Continue with more complex schedules
Once the basic formula is understood, review how extra payments, changing rates, and balloon maturities alter later rows.
Build and compare the schedule
Use the free amortization calculator for a standard schedule. Use the registered Windows amortization software when you need to edit individual dates, payments, rates, or notes and save the revised loan.