The formula
- P
- Original principal
- i
- Periodic interest rate
- n
- Total number of payments
- PMT
- Level periodic payment
Worked example: $100,000, 6%, 30 years
For monthly payments, the periodic rate is 0.06 ÷ 12 = 0.005 and the number of payments is 30 × 12 = 360.
Each month, interest equals the beginning balance times 0.005. Principal equals the payment minus that month’s interest. The ending balance becomes the next month’s beginning balance.
How principal and interest change
The total payment can remain constant while its composition changes. Early payments contain more interest because the balance is larger. As principal falls, the interest portion declines and more of the payment reduces principal.
How extra payments change amortization
An extra principal payment reduces the balance immediately. If the regular payment continues unchanged, later interest is calculated on the smaller balance and the loan normally pays off sooner.
When the standard formula does not apply
Irregular payment dates, changing rates, skipped payments, negative amortization, construction draws, and other non-level cash flows require a row-by-row calculation rather than a single closed-form payment formula.
Check the math with a calculator
Enter your own numbers in the matching Power of Interest calculator. The calculator performs the arithmetic while this page explains the formula and assumptions behind it.