Remaining Loan Balance Calculator

What this calculator does

An amortising loan has a fixed monthly payment that splits between interest on the remaining balance and principal repayment. The interest portion is largest at the start (because the balance is largest) and smallest at the end. As a result, the remaining balance does not fall linearly with the number of payments made — it falls slowly at first and faster later. This calculator takes the original principal, annual rate, original term in months, and the number of payments already made, and returns the remaining balance plus a breakdown of how much of the cumulative payments has gone to principal versus interest.

The formula

The remaining balance after n payments is given by B = P(1+r)ⁿ − M × ((1+r)ⁿ − 1) ÷ r, where P is the original principal, r is the monthly rate (annual rate ÷ 12, decimal), M is the standard amortising monthly payment, and n is the number of payments already made. The first term is what the principal would have grown to if no payments were made; the second term is the future-value annuity of the payments at the same rate. The difference is the actual remaining balance under standard amortisation accounting — the same convention every lender uses.

Worked example

Take a 15,000 loan at 10% annual rate over 36 months with 12 payments made. The monthly rate is 10 ÷ 12 = 0.833%. The standard amortisation formula produces a monthly payment of approximately 484.01. After 12 payments, the remaining balance is about 10,488.86. Cumulative payments total about 5,808.09, of which about 4,511.14 has gone to principal and about 1,296.96 to interest. After one third of the term, only about 30% of the principal has been paid down — front-loaded interest is the reason.

How the principal-vs-interest split shifts over time

On the same 15,000 loan at 10% over 36 months, the per-payment split moves steadily from interest-heavy to principal-heavy as the balance falls. The first payment is approximately 125.00 interest and 359.01 principal. By the twelfth payment the split is approximately 90.69 interest and 393.32 principal. By the twenty-fourth it is approximately 49.47 interest and 434.54 principal. The thirty-sixth (final) payment is approximately 4.00 interest and 480.01 principal. Total interest across the loan life is the sum of all these interest portions; total principal is the original 15,000 returned to the lender across the same payments.

Why the balance falls slowly at first

At month 12 of a 36-month 10% loan, cumulative payments of about 5,808.09 have reduced the principal by 4,511.14 — the other 1,296.96 went to interest. By month 24, cumulative payments of about 11,616.19 have reduced the principal by about 9,494.65, leaving a remaining balance of about 5,505.35. The principal-reduction pace accelerates as the loan ages because each payment's interest portion shrinks with the balance, leaving more for principal. This is the standard shape of every amortising loan.

What this calculation does not capture

Extra payments toward principal during the loan life — if the borrower has paid more than the scheduled monthly amount, the actual remaining balance is lower than this calculator returns. Variable-rate loans where the rate has changed during the term — the formula assumes a fixed rate held for the entire life of the loan to date. Fees added to principal during the loan, such as capitalised late charges on some commercial loans. For an exact payoff figure including per-day interest from the last payment date to the payoff date, request a payoff quote from the lender.

When to use the remaining-balance figure

For a refinance decision, the remaining balance is what a new loan needs to cover. For early payoff, the balance plus a small amount of accrued daily interest is the cash needed. For selling a financed asset, the balance is the lien payoff. For mortgage tax preparation in jurisdictions that allow interest deduction, the year-over-year change in balance shows principal reduction for the year. Each of these cases benefits from the exact remaining balance rather than an approximation based on payment count.