How to Calculate a Loan Payment by Hand
The exact formula lenders use to set a fixed loan payment, worked through with real numbers.
Every fixed-rate installment loan — personal, auto, student, business — uses the same payment formula. Here it is worked through with actual numbers instead of just letters.
The formula
Payment = P × r × (1 + r)^n ÷ ((1 + r)^n − 1), where P is the loan amount, r is the periodic interest rate (your APR divided by the number of payments per year), and n is the total number of payments.
Worked example
Say you borrow $15,000 at 9% APR for 4 years, paid monthly.
- Periodic rate: 9% ÷ 12 = 0.75%, or 0.0075 as a decimal.
- Total payments: 4 years × 12 = 48.
- (1 + 0.0075)^48 ≈ 1.4320.
- Payment = 15,000 × 0.0075 × 1.4320 ÷ (1.4320 − 1) ≈ $373.28 a month.
Over 48 payments that's $17,917.44 paid total, meaning $2,917.44 of it is interest.
Why the formula looks the way it does
The (1 + r)^n term is compound growth — what the balance would become if you paid nothing at all. Dividing by that same term minus 1 spreads the loan's total compounding evenly across every payment, so the payment is constant instead of shrinking or growing over time. Solve the same formula for a different n (say, weekly instead of monthly payments) and you'll get a smaller per-payment number, since interest has less time to build between payments.
Skip the arithmetic and plug your own numbers into the Loan Calculator.