Amortization Formula
On this page
The level-payment formula solves the periodic payment that reduces a fixed-rate principal to zero over a stated number of periods.
Payment equation
M = P × r(1+r)^n / ((1+r)^n − 1). P is principal, r is the periodic note rate, n is number of payments, and M is periodic principal and interest. When r is zero, use M = P/n to avoid division by zero.
Schedule equations
For period t: interest_t = balance_(t-1) × r; principal_t = payment_t − interest_t; balance_t = balance_(t-1) − principal_t − extra_t. Cap the last payment and principal at the amount needed to clear the balance.
Rate and period alignment
The rate period must match the payment period. A monthly schedule using a nominal annual note rate commonly uses annual rate / 12. Do not divide APR by 12 and call it the contractual rate.
Worked substitution
For $10,000 at 6% over 36 monthly payments, r = 0.06/12 and n = 36. The formula gives about $304.22. First-month interest is $50.00 and first-month principal is about $254.22 before contract-specific rounding.
Reconciliation checks
The sum of principal must equal the original principal; ending balance must be zero; total payments minus principal must equal total interest within the declared rounding convention. Test zero rate, one period, and final-cent behavior.
Frequently asked questions
Why is my spreadsheet off by cents?
It may round each row differently or use a different final-payment adjustment.
Is the formula compound interest?
It is the standard annuity relationship for a periodic amortizing balance.
Can I use it for irregular payments?
Not without a cash-flow schedule that models every date and amount.
What rate goes into r?
The periodic note rate aligned to the payment convention.
Sources
- CFPB amortization explanation: https://www.consumerfinance.gov/ask-cfpb/what-is-amortization-and-how-could-it-affect-my-auto-loan-en-771/
- CFPB interest rate vs APR: https://www.consumerfinance.gov/ask-cfpb/what-is-the-difference-between-a-mortgage-interest-rate-and-an-apr-en-135/
- CFPB mortgage servicer rules: https://www.consumerfinance.gov/consumer-tools/mortgages/your-mortgage-servicer-must-comply-with-federal-rules/
Source research checked September 11, 2026. CalculatorGeek Algorithmic Team completed the calculation, source, and content review on September 11, 2026. This page provides educational estimates, not lending, legal, tax, or financial advice.
Use this resource
Keep exploring