A remaining loan balance calculator answers one narrow question: after a given number of scheduled payments on an amortising loan, how much principal is still owed? It is arithmetic, not a lookup. Given the original amount, the rate, the term and the number of payments made, the outstanding principal is fully determined, and this page computes it along with how much of what you have paid so far went to interest rather than to the debt itself.
Arb Digital publishes it in a free tools library that already contains a loan calculator for working out the payment in the first place and a loan amortization schedule for printing the whole table period by period. The boundary is deliberate. Those pages build the schedule; this one jumps straight to a single row of it, which is what you want when the question is simply how much is left. And it is worth saying at the outset: the figure on your lender's statement, and the payoff quote your servicer issues, are the numbers that actually govern your debt. This page reproduces the standard formula from the inputs you type.
What This Remaining Loan Balance Calculator Does
It first derives the scheduled payment from the original amount, the periodic rate and the number of periods in the term. Then it steps through the payments you say have been made, charging interest on the balance in each period and applying the payment against it. What is left at the end of that walk is the outstanding principal.
Alongside it you get three supporting figures. The principal repaid so far is simply the original amount minus the balance. The interest paid so far is everything else you have handed over, and on a long loan early in its life that number is startling. The payoff estimate adds interest accrued since the last payment date, because a balance and a payoff amount are not the same thing.
The extra-payment field lets you model a loan where you have been paying more than the schedule requires. When it is non-zero, the page walks the payments one at a time rather than using the closed-form expression, so the answer stays exact rather than approximate.
What the page cannot do is know your account. Fees, escrow, missed payments, forbearance, capitalised interest and rate changes sit outside the model, and where they apply the lender's figure is right and this one is an approximation.
How to Use It
- Enter the amount financed, not the price. If you put money down or rolled fees into the loan, the starting principal is the amount the lender actually advanced, which is on the loan agreement rather than the sale contract.
- Use the note rate, not the annual percentage rate. The APR includes fees and is designed for comparing offers. Interest accrues at the note rate, so that is the figure the schedule is built from. The APR calculator handles the conversion in the other direction.
- Count payments made, not months elapsed. Those are different numbers if any payment was missed, deferred or paid twice, and the balance follows the payments.
- Set the frequency to match the loan. A loan billed every two weeks makes twenty-six payments a year, and treating it as monthly produces a balance that is wrong in both directions at once.
- Add the days since your last payment only if you want a payoff estimate. Leave it at zero to see the balance exactly as it stands the moment a payment posts.
The Formula / How It's Calculated
The scheduled payment on a fully amortising loan is
M = P × i ÷ (1 − (1 + i)−n), where P is the original principal, i is the rate for one period and n is the number of periods in the full term.
The balance after k payments is then
Bk = P × (1 + i)k − M × ((1 + i)k − 1) ÷ i.
Read that as two competing quantities. The first term is what the original debt would have grown to with no payments at all. The second is what your payments have grown to, treated as a series earning the same rate. The balance is the gap between them, which is why it closes so slowly at first and so quickly at the end.
Worked example, matching the values this page loads with. A loan of 250,000 at 6.5 per cent over 30 years, monthly. The periodic rate is 0.065 ÷ 12 = 0.00541667 and n is 360, so the payment is 1,580.17. After 60 payments, (1 + i)60 = 1.382796, so the first term is 250,000 × 1.382796 = 345,699. The annuity factor is (1.382796 − 1) ÷ 0.00541667 = 70.6700, so the second term is 1,580.17 × 70.6700 = 111,671. The balance is 345,699 − 111,671 = 234,027.44.
That means five years of payments totalling 94,810 have reduced the debt by 15,972. The other 78,838 was interest. Adding twelve days of accrued interest at a daily rate of 0.065 ÷ 365 gives 500.11, so the payoff estimate is 234,527.56. Stepping the loop through all sixty periods one at a time produces the same balance to the cent, which is the check that the two methods agree.
Why Your Balance and Your Payoff Amount Are Different Numbers
This is the single most common surprise, and it is not an error on anyone's part. The balance is the principal outstanding as at the last posted payment. The payoff amount is what it would take to close the account on a specific future date, and it therefore includes interest that has accrued since that payment, any fees charged and not yet paid, and in some agreements a prepayment charge.
The Consumer Financial Protection Bureau makes the distinction directly in its explanation of what a payoff amount is and whether it is the same as your current balance, and notes that for a loan secured by a dwelling the servicer must supply an accurate statement of the total needed to pay the loan in full as of a date you specify. That statement, not any calculator, is the figure that settles the debt.
The gap also moves every day, so a payoff quote is good only through a stated date. Send the quoted amount a week late and a small balance remains, which is how people end up with an unexpected final bill on a loan they believed was cleared.
Why the Balance Falls So Slowly at the Start
Nothing is being withheld from you. In the first period, interest is charged on the entire original principal, and on a long loan at a normal rate that interest consumes most of the payment. In the worked example above the first month's interest is 1,354.17 against a payment of 1,580.17, so only 226 goes to principal. By the final month the interest charge is a few dollars and almost the whole payment is principal.
The CFPB describes this pattern in its guide to how paying down a mortgage works: early payments are interest-heavy because the balance is high, and the split shifts steadily toward principal as the balance falls. The shape is a consequence of the arithmetic, not a policy choice by the lender.
One practical implication is that the halfway point in time is nowhere near the halfway point in principal. On a thirty-year loan at a typical rate the balance does not fall to half the original amount until somewhere around year twenty. Anyone budgeting on the assumption that fifteen years of payments has cleared half the debt will be a long way out. The mortgage amortization calculator shows that crossover explicitly.
What Breaks the Standard Formula
The closed-form balance assumes a specific, tidy loan: fixed rate, equal payments, interest charged on the balance once per period, every payment made on time. Real loans deviate in several well-known ways, and each one moves the true balance away from the computed one.
Daily simple interest. Many car loans and personal loans accrue interest per day rather than per period. Pay a few days late and more of that payment goes to interest, so principal falls by less than the schedule says; pay early and the opposite happens.
Interest-only or deferred periods. If the loan began with a period where only interest was charged, or where nothing was charged and interest capitalised, the balance at the start of amortisation is not the original advance. Enter the capitalised balance and the remaining term as the starting point instead.
Rate changes. On a variable or adjustable loan the payment is recalculated at each reset against the balance and remaining term at that moment. A single-rate model can only approximate it. Run the calculation in segments, using the balance at each reset as the new starting principal.
Escrow and bundled costs. On a mortgage the amount you send is often principal, interest, taxes and insurance together. Only the principal-and-interest portion belongs in this calculation. Using the full payment overstates repayment substantially.
Payments applied to the wrong place. An extra amount is not automatically applied to principal. Some servicers hold it as a prepayment of the next instalment, which changes nothing about the balance. If extra payments are the point, the instruction to apply them to principal usually has to be explicit. The extra payment loan calculator models what correct application achieves.
Extra Payments and What They Actually Change
An extra payment applied to principal removes that amount from the balance permanently, and every future interest charge is calculated on a smaller number. The saving is therefore not the extra payment itself but all the interest it prevents for the rest of the term, which is why the effect is much larger earlier in the loan.
What an extra payment normally does not change is the scheduled payment. On a standard fixed-rate loan the instalment stays the same and the term shortens instead. If a lower monthly payment is the objective rather than a shorter term, that requires a recast or a refinance, which are different transactions with their own conditions and costs. The mortgage recast calculator covers the first of those.
There is also an order-of-operations point when several debts exist. The balance on any one loan is only part of the picture, and the rate matters more than the size when deciding where a spare payment does the most work. Reducing a set of debts to one equivalent figure is what the blended interest rate calculator does, and the loan payoff calculator projects a single debt to its end date.
Arb Digital publishes a large library of free financial and business tools, all of them free to use and free of sign-up.
Browse the Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Treating the computed balance as a payoff figure — accrued interest, unpaid fees and any prepayment charge sit on top of it, and only the servicer's statement is binding.
- Entering the full mortgage payment including escrow — taxes and insurance never touch the principal, so including them makes the loan look years ahead of where it is.
- Using the APR instead of the note rate — the APR bundles fees for comparison purposes; interest accrues at the note rate and the schedule is built from it.
- Counting months rather than payments made — a deferred or missed payment leaves the balance higher than the calendar suggests, and capitalised interest can leave it higher than the original advance.
- Assuming extra money went to principal — unless the servicer was instructed otherwise it may have been held against the next instalment, which does not reduce the balance at all.
Related Free Tools From Arb Digital
Work out the payment in the first place with the loan calculator, print the full table with the loan amortization schedule, and see the principal crossover on a home loan with the mortgage amortization calculator. Project a debt to its end date with the loan payoff calculator, test overpayments with the extra payment loan calculator, model a re-amortisation with the mortgage recast calculator, convert a rate plus fees with the APR calculator, and reduce several debts to one rate with the blended interest rate calculator. The rest are in the free online tools hub.
Frequently Asked Questions
Take the original principal grown at the periodic rate for the number of payments made, then subtract the future value of the payments made at that same rate. In symbols the balance after k payments is P times (1 + i) to the power k, minus the payment times ((1 + i) to the power k minus 1) divided by i.
Because early payments are mostly interest. In the worked example on this page, five years of payments totalling 94,810 reduced a 250,000 loan by only 15,972. The split shifts toward principal steadily, but the first years barely move the balance at all.
No. The payoff amount adds interest accrued since the last posted payment, any unpaid fees and any prepayment charge in the agreement. For a loan secured by a dwelling the servicer must give you an accurate payoff statement as of a date you specify, and that figure is the one that settles the debt.
It works for any fully amortising loan with a fixed rate and equal payments. Many car and personal loans accrue interest daily rather than per period, so paying late or early shifts the split between interest and principal and the real balance drifts from the schedule.
An extra amount applied to principal reduces the balance immediately and every later interest charge with it, so the term shortens while the scheduled payment stays the same. It only works if the servicer applies it to principal rather than holding it against the next instalment.
A single-rate model cannot represent that exactly. Run the calculation in segments: compute the balance up to the reset date at the old rate, then start a new calculation using that balance as the principal, the new rate and the remaining term.
Much later than halfway through the term. At typical rates the balance on a thirty-year loan does not fall to half the original amount until somewhere around the twentieth year, because the interest share of each payment is so large in the early years.
Your statement, always. This page reproduces the standard formula from the numbers you type. Your lender applies your actual payment history, fees, escrow and any rate changes, and its records govern what you owe.
This page performs arithmetic on figures you enter and is provided for general information only. It is not financial advice, not an offer of credit, and not a statement of what you owe. The balance, payoff amount, fees and terms that govern your loan are those held by your lender or servicer and set out in your loan agreement, and a payoff statement from the servicer is the only figure that settles an account. For advice about your own circumstances, speak to a licensed financial adviser or an accredited non-profit credit counsellor.
