Money formula
Loan Payment Formula
Learn the fixed-payment loan formula used for amortizing installment loans.
Formula
Payment = P × r(1+r)^n ÷ ((1+r)^n − 1)What the formula means.
An amortizing loan uses a periodic interest rate and fixed number of payments to calculate one regular payment that pays interest and reduces principal over time.
Rate and payment period must match.
Fees are not part of the standard principal-and-interest formula unless added to principal.
Extra payments can change payoff time and total interest.
Variables.
PPrincipal
Amount borrowed.
rPeriodic rate
Interest rate for each payment period.
nPayments
Total number of scheduled payments.
Worked example.
$25,000 at 7% for 5 years
- Monthly rate = 0.07 ÷ 12
- Payments = 5 × 12 = 60
- Apply the amortizing payment formula
Try your own numbersLoan Payment Calculator
↗Common mistakes.
- Using APR details that include fees as though they were a simple nominal rate without checking definitions.
- Mixing annual rate with monthly n.
- Assuming every lender applies extra payments the same way.
Quick questions.
Is this the same formula used for mortgages?
For a standard fixed-rate amortizing balance, the principal-and-interest relationship is the same.
What happens when interest is zero?
Payment becomes principal divided by the number of payments.