Loan Remaining Balance Calculator
Find the outstanding balance of an amortizing loan after any number of payments, using the closed-form balance formula.
How it works
Balance = P·(1 + i)^k − PMT·[(1 + i)^k − 1] / i · k = payments made
The remaining balance equals the original principal grown by interest for k periods, minus the future value of the payments already made. This closed-form expression gives the payoff figure directly, without building a full amortization schedule row by row. It is exactly the balance a lender would quote for an early payoff before that period’s interest accrues.
Worked example
On a $200,000 loan at 6% (0.5% monthly) over 360 months, the payment is $1,199.10. After 60 payments (5 years), balance = 200,000·1.005^60 − 1,199.10·[1.005^60 − 1]/0.005 = 269,861 − 83,684 = $186,177 — only about $14,000 of principal repaid in five years.
Sources: Amortization calculator — Wikipedia
Frequently asked questions
Why is so little principal gone after five years?
Early in an amortizing loan most of each payment covers interest on the large outstanding balance, so principal falls slowly at first and much faster near the end of the term.
Is this the exact payoff amount?
It is the scheduled balance right after the k-th payment. An actual payoff quote may add accrued interest to the payoff date and any fees, so confirm the exact figure with the lender.
What if I have made no payments yet?
Enter 0 payments made and the remaining balance equals the original loan amount, with 0% repaid. The formula handles that boundary cleanly.
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Educational financial-math tool, not investment or financial advice.