The loan payment formula
Most personal, student and small business loans are fully amortizing, which means you pay the same amount every month and the loan is paid off exactly at the end of the term. The payment is found with M = P × r × (1 + r)^n ÷ ((1 + r)^n − 1), where P is the amount borrowed, r is the monthly rate (APR ÷ 12 ÷ 100) and n is the number of months. Borrowing $10,000 at 5% for 60 months gives a payment of $188.71, and you repay $11,322.74 in total, so the loan costs $1,322.74 in interest.
If the interest rate is zero, the formula simplifies to the amount divided by the number of months, which the calculator handles automatically.
Why APR matters more than the payment
Lenders often advertise a low monthly payment by stretching the term. A $15,000 loan at 8% costs $304.15 a month over 5 years but only $233.79 over 7 years. The lower payment looks attractive, yet the 7-year loan costs about $4,639 in interest compared with $3,249 for the 5-year loan. Always compare the total interest and the APR, which includes most fees, rather than the payment alone. Watch for origination fees that are deducted from the amount you receive; they effectively raise the cost of borrowing.
Paying extra each month
Any amount you pay above the required payment goes straight to principal, which reduces the interest charged in every following month. Enter an extra monthly payment and the calculator re-runs the schedule to show your new payoff time and the interest you save. On a $15,000, 8%, 60-month loan, paying an extra $50 a month clears it about 10 months early and saves roughly $560. Before paying extra, check that your loan has no prepayment penalty and ask the lender to apply the extra to principal rather than to future payments.
What this calculator assumes
The results assume a fixed rate, monthly payments and interest calculated on the remaining balance each month, which is how most installment loans work. Some loans differ: credit cards and lines of credit have variable rates and minimum payments; payday and some auto loans use precomputed interest; interest-only loans do not reduce the balance at first. Student loans may have grace periods or income-driven payments. For those, use this tool as a rough comparison and check the loan agreement for the exact terms. Small differences between our figures and your lender’s are usually due to rounding or the exact day interest is charged.
Frequently asked questions
How is a monthly loan payment calculated?
With the amortization formula M = P × r × (1 + r)^n ÷ ((1 + r)^n − 1), using the monthly rate and the number of months.
Does paying extra on a loan save money?
Yes. Extra payments reduce the principal, so you pay less interest and finish sooner, as long as there is no prepayment penalty.
What is the difference between interest rate and APR?
The interest rate is the cost of borrowing the principal. APR adds most fees, so it is the better number for comparing loans.
Why is my lender’s payment slightly different?
Lenders may round differently, charge interest daily, or include fees in the loan amount.