How this calculator works
A fixed-rate loan credits each payment first to the interest charged on the opening balance and then to principal. Early payments are mostly interest, so the balance falls slowly at first and speeds up later. This calculator applies the closed-form balance formula after the number of payments you enter, assuming every payment was made on time and in full, at the original rate, with no extra payments. The result matches a lender payoff statement only if the lender uses the same monthly convention and applies no fees or unpaid interest.
Formula
i = annual rate / 12; A = P × i / (1 - (1 + i)^(-n)); balance after k payments B = P × (1 + i)^k - A × ((1 + i)^k - 1) / i. Principal repaid = P - B. Interest paid = k × A - (P - B). Share repaid = (P - B) / P.
Worked example
A $25,000 loan at 6% over 60 months has a payment of $483.32. After 24 payments the balance is $15,887.22. Principal repaid is $9,112.78, or 36.45% of the loan, while $2,486.90 of interest has been paid. Forty percent of the payments have been made but only about a third of the principal is gone, which shows how front-loaded interest is.
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Frequently asked questions
Why is the balance higher than the loan amount minus the payments?
Because part of every payment covers interest, which does not reduce the loan. Only the principal portion lowers the balance, and that portion is smallest at the start.
Does this match my payoff statement?
Closely, if the rate and term are right and no extra payments or fees were applied. Lenders may use daily interest accrual and round payments to cents, which produces small differences.
What if I made extra payments?
The closed-form balance assumes only the regular payment. Use the early loan payoff calculator to model extra payments and see how the term shortens.
Can I enter a term that is not a whole number of months?
The term is a whole number of monthly payments. For another frequency, calculate the payment with the periodic loan calculator first and then apply the same recurrence.