How a fixed loan payment works
Most fixed-payment loans — personal loans, student loans, and many others — work the same way: the amount borrowed, plus interest, gets split into equal payments over the term. Early in the loan, a larger share of each payment is interest on the outstanding balance, and that share shrinks over time until the last payment, which is almost entirely principal.
Formulas used
Monthly payment: P = L × i ÷ (1 − (1 + i)^−n)
Maximum loan amount (from a payment): L = P × (1 − (1 + i)^−n) ÷ i
Term needed (from a payment): n = −log(1 − L × i ÷ P) ÷ log(1 + i)
Where L is the loan amount, i is the monthly interest rate (annual rate divided by 12 and by 100), n is the number of payments, and P is the payment amount.
Practical example
A $10,000 loan at a 9% annual rate over 36 months comes out to a monthly payment of roughly $318, totaling around $11,440 paid by the end — about $1,440 of that in interest. If you wanted to keep the payment at $350 instead, with the same rate and term, you could borrow up to roughly $11,000, a bit more than in the example above.
Why the minimum payment has to cover the interest
If the payment you choose is smaller than the interest generated by the balance in the first month, the loan will never get paid off — the balance grows every month instead of shrinking. That's why, when calculating the term needed for a specific payment, that payment has to be larger than the loan amount times the monthly interest rate; otherwise there's no term that solves the equation.
A longer term lowers the payment but raises the total cost
Stretching out a loan's term lowers each payment, which can be necessary to fit a monthly budget, but it usually increases the total interest paid over the life of the loan, since the balance stays higher for longer and keeps accruing interest. It's always worth comparing the total paid across different terms before deciding, not just the payment amount on its own.
What this calculator doesn't account for
This simulation doesn't include origination fees, loan insurance, or other charges some lenders add on top of the stated interest rate, which increase the effective cost of borrowing beyond what's shown here. Treat the results as a planning estimate, and always confirm the full cost — including fees — before signing.