Loan balance after a given number of payments

Why Remaining Balance Is Not What You Expect

Loan amortisation front-loads interest. After 12 payments on a typical 36-month loan at 10%, you have paid roughly 5,800 but reduced principal by only 3,800 — the other 2,000 was interest. After 24 of 36 payments, you have paid 11,600 but reduced principal by 8,000. The remaining balance does not drop linearly with payments made. This calculator shows exactly where you stand at any point in the loan.

When This Matters

Refinancing decisions — the remaining balance is what a new loan needs to cover. Early payoff — knowing the balance tells you whether you have the cash to clear the loan. Selling financed assets (car, equipment) — the balance is the lien payoff amount. Tax calculations — mortgage interest paid in a tax year is a deduction in some jurisdictions; this tool reveals the split. Selling a home before the loan matures — the remaining mortgage balance determines net proceeds.

The Formula Explained

Remaining balance after n payments equals P(1+r)^n - M × ((1+r)^n - 1) / r, where P is original principal, r is monthly rate, M is monthly payment, and n is payments made. The first term is what principal would have grown to at the rate without payments; the second term is what the payments have accumulated to in a compound-interest sense. Subtracting gives the actual remaining balance. This is standard amortisation accounting used by every lender.

Principal vs Interest Split Over Time

First payment on a 36-month 10% loan on 15,000: monthly payment 484, interest portion 125, principal portion 359. Twelfth payment: interest portion 93, principal portion 391. Twenty-fourth payment: interest portion 54, principal portion 430. Thirty-sixth payment: interest portion 4, principal portion 480. The split shifts substantially as the loan ages — which is why small extra principal payments early in the loan save disproportionate interest.

Worked Example

15,000 loan at 10% over 36 months, 12 payments made. Monthly payment: 484. Remaining balance: approximately 11,194. Principal paid: 3,806. Interest paid: 2,003. Total paid: 5,809. Note that after one-third of the term, you have paid off only one-fourth of the principal, because early payments are heavily weighted toward interest. After 24 payments (two-thirds through), you will have paid 8,000 of principal and only 3,194 remains — the principal reduction accelerates in the back half of the loan.

What This Tool Does Not Show

Prepayments — if you have paid extra toward principal during the loan, your remaining balance is lower than this calculator shows. Variable-rate loans where the rate has changed during the term. Fees added to principal during the loan (some commercial loans capitalize late fees). For precise payoff, request a loan payoff quote from your lender which includes per-day interest up to the exact payoff date.

Practical Uses of Remaining Balance

Before refinancing, knowing the balance tells you whether refinance math works. Before selling a financed asset, the balance is the payoff required from sale proceeds. Before paying off a loan early, the balance shows the cash needed plus prorated interest. For tax preparation, the balance at year start vs year end shows principal reduction for the year. Each of these uses benefits from the exact balance rather than a rough guess based on payment count.