Loan Payoff Calculator
Balance, APR & payment
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Fill in the fields on the left and this updates as you type.
Know what this estimate is based on
- Jurisdiction
- United States card and lending practice
- Scope and limitations
- Educational estimate only. Your issuer sets the minimum-payment formula, how a payment is allocated across balances, when interest is charged, and any fees or promotional terms — check your cardholder agreement for the figures that bind.
- Source links checked
- Jul 30, 2026
Built and regression-tested by Smart Tools Lab. It has not been individually reviewed by a licensed financial, tax, or legal professional.
How to use
- 01
Enter the loan balance and interest rate.
- 02
Enter your fixed monthly payment.
- 03
See how long payoff takes and the total interest.
Formula
i = APR ÷ 12 (the monthly rate, so 9% → 0.0075). months = −ln(1 − balance × i ÷ payment) ÷ ln(1 + i). total interest = payment × months − balance. The payment must be greater than balance × i (the first month's interest); if it is not, the balance never falls and there is no payoff time.
Example
Inputs: balance $15,000, annual rate 9%, payment $400 per month. Step 1 — monthly rate: i = 9 ÷ 12 = 0.75% = 0.0075. Step 2 — first month's interest (the floor): $15,000 × 0.0075 = $112.50. The $400 payment is well above this, so the loan does amortize. On the first payment, $112.50 covers interest and $287.50 (72%) reduces the balance. Step 3 — months: balance × i ÷ payment = $15,000 × 0.0075 ÷ $400 = 0.28125. Then 1 − 0.28125 = 0.71875. ln(0.71875) ≈ −0.330242 and ln(1.0075) ≈ 0.007472. months = −(−0.330242) ÷ 0.007472 ≈ 44.20. Step 4 — because 44.20 is not a whole number, the loan clears after 44 full payments plus a small partial payment in month 45 — about 3.7 years. Step 5 — total interest: $400 × 44.20 − $15,000 ≈ $2,679. Result: paid off in roughly 44 months (just under four years) at a cost of about $2,679 in interest — 15% of everything you hand over. Raise the payment 10%, to $440, and the same loan clears about five months sooner and saves roughly $290.
Definitions
- Balance
- The amount still owed on the loan today. Interest each month is charged on this figure, so it is the number the payoff plan is trying to drive to zero.
- Monthly rate (i)
- The annual interest rate divided by 12. A 9% annual rate is a 0.75% (0.0075) monthly rate, and it is the rate actually applied to the balance each month.
- Interest floor
- The first month's interest charge, equal to balance × monthly rate. A payment at or below this floor never reduces the balance, so the loan can never be repaid.
- Total interest
- The full interest cost of the loan, found as payment × months − balance. It rises sharply as the payment falls toward the interest floor and shrinks fast as the payment rises.
- Amortization
- The process by which a fixed payment gradually retires a loan: each payment covers that month's interest first, and whatever is left reduces principal, which lowers next month's interest.
- Payoff time
- The number of months (and years) until the balance reaches zero at a fixed payment, computed directly from the balance, monthly rate, and payment.
Good to know
What this calculator answers
This tool answers one precise question: at a fixed monthly payment, how long does an existing installment loan take to reach zero, and how much interest do you pay along the way? You supply three numbers — the current balance, the annual interest rate, and the amount you intend to pay every month — and the calculator returns the payoff time in months and years plus the total interest cost. It assumes the payment never changes and the rate stays fixed for the life of the loan. Using the default inputs, a 500,000 balance at a 9 percent annual rate with a 12,000 monthly payment clears in roughly 50 months, a little over four years, while costing about 101,755 in interest. The power of the tool is what it reveals when you nudge the payment: because interest is charged on whatever balance remains, every extra unit you pay each month attacks principal directly and pulls the finish line closer. The result is not a payment schedule or a comparison of competing offers — it is a clean read on the timeline and total cost implied by the single payment figure you choose. That makes it the natural starting point for anyone holding a loan who wants to know, before changing anything, exactly where the current plan leads and how much room there is to do better by paying more.
The payoff formula, step by step
The engine solves for the number of payments directly. First it converts the annual rate into a monthly rate by dividing by twelve: i = APR divided by 12. A 9 percent annual rate becomes a monthly rate of 0.0075, or 0.75 percent. Then it finds the month count with months = minus the natural log of (1 minus balance times i divided by payment), all divided by the natural log of (1 plus i). The natural log appears because the balance shrinks geometrically — each month the remaining principal is multiplied by (1 plus i) and then reduced by the payment — and solving that repeating relationship for the number of steps produces a logarithm. Once the month count is known, total interest is simply payment times months minus the balance, since every unit you hand over either covers interest or retires principal, and only the principal repays the original balance. There is one hard requirement hidden in the formula: the term inside the first logarithm, 1 minus balance times i divided by payment, must stay positive. That is only true when the payment is larger than balance times i, the first month's interest charge. If the payment equals or falls below that interest charge, the logarithm is undefined and the loan never amortizes. Everything the calculator reports flows from these two compact expressions, so understanding them is enough to predict how any change to your inputs will move the answer.
Walking through the default example
Take the defaults and follow the arithmetic by hand. The balance is 500,000, the annual rate is 9 percent, and the payment is 12,000 per month. The monthly rate is 9 divided by 12, which is 0.75 percent, written as 0.0075. The first month's interest is 500,000 times 0.0075, or 3,750 — so on the very first payment, 3,750 covers interest and the remaining 8,250 reduces the balance. Plugging into the month formula, balance times i divided by payment is 500,000 times 0.0075 divided by 12,000, which equals 0.3125. One minus 0.3125 is 0.6875, and its natural log is about minus 0.3747. The natural log of 1.0075 is about 0.007472. Dividing minus 0.3747 by 0.007472 and flipping the sign gives roughly 50.15 months. Because that is not a whole number, the loan is gone after the 50th full payment plus a small final payment in month 51. Total interest is 12,000 times 50.15 minus 500,000, which works out to about 101,755. Notice the contrast between the start and the end: the first payment is only 69 percent principal, while the last payments are almost entirely principal because there is barely any balance left to charge interest on. The same mechanics apply to any balance, rate, and payment you enter — only the numbers change.
The threshold where a loan never dies
Every loan has a floor payment below which it cannot be repaid, no matter how patient you are. That floor is the first month's interest charge: balance times the monthly rate. With the default 500,000 balance at 9 percent, the monthly rate is 0.0075, so the floor is 3,750. Pay exactly 3,750 and the entire payment is swallowed by interest, leaving the balance untouched forever — an interest-only standstill. Pay even slightly more and the loan does eventually clear, but the timeline near the floor is brutally long. A payment of 3,800, just 50 above the interest charge, takes about 580 months — more than 48 years — to retire the balance. Raise it to 4,000 and the term drops to about 371 months, roughly 31 years. The sensitivity here is extreme because the tiny sliver above the interest charge is all that touches principal, and early on that sliver is minuscule. This is exactly why the calculator refuses to return a timeline when your payment sits at or below the floor: there is no finite answer to report. The practical lesson is that minimum payments set close to the interest charge are a trap. The first goal of any payoff plan is simply to clear the floor by a comfortable margin, because the distance between your payment and the monthly interest charge is the engine that actually moves the balance down.
Why paying more shrinks the timeline so fast
The relationship between your payment and your payoff time is steeply non-linear, which is the single most useful insight this calculator delivers. Doubling your payment does not merely halve the term — it cuts it by far more, and it slashes total interest even harder. Start from the default: 12,000 a month clears the 500,000 balance in about 50 months with roughly 101,755 of interest. Now compare neighboring payment levels on the same loan. Pay only 6,000 a month and the term stretches to about 131 months, nearly 11 years, with interest ballooning to about 287,602 — nearly three times the cost for half the payment. Push the payment up to 24,000 a month and the loan is gone in about 23 months with only about 45,713 of interest. The reason is compounding working in reverse: every extra unit you pay this month shrinks the balance that next month's interest is calculated on, which leaves more of next month's payment free to attack principal, and so on in a self-reinforcing loop. Small, early increases compound into large savings because they act for the entire remaining life of the loan. This is also why front-loading matters — an increase you make now is worth more than the same increase made years from now, simply because it has more months to keep cutting the interest base. The takeaway is that even modest, sustainable bumps to a fixed payment pay outsized dividends.
The impact of a one-off extra payment
A single lump sum, applied directly to principal, behaves differently from raising your monthly payment, but it can be just as powerful — especially when it lands early. Suppose you keep paying the default 12,000 a month but make a one-off extra payment of 50,000 today, dropping the balance from 500,000 to 450,000. From that point the same payment retires the smaller balance in about 44 months instead of 50, and total interest falls from roughly 101,755 to about 80,366. That single 50,000 payment saved you close to 21,389 in interest — meaning the lump sum effectively earned a return equal to the loan's rate, compounded, for every month it stayed off the balance. The earlier the lump arrives, the more it saves, because it removes principal that would otherwise have accrued interest across the entire remaining term. A windfall, bonus, or tax refund directed at the balance does double duty: it shortens the timeline and reduces the interest base for every payment that follows. To model this with the calculator, simply subtract the lump from your current balance and re-run the numbers at your usual payment; the new term and interest figures show exactly what the one-off payment bought you. Before sending a lump sum, confirm with the lender that extra payments are applied to principal rather than held against future installments, and that no prepayment penalty applies.
Reading the timeline in months and years
The calculator reports the payoff time both as a number of months and as a span of years, and the two views serve different purposes. The month count is the precise output of the formula and is often a fraction — the default works out to about 50.15 months. That fractional tail matters because it tells you the loan is not gone after a clean 50 payments; there is a small partial payment in the following month to mop up the last sliver of balance. If you multiplied a rounded 50 months by the 12,000 payment you would get 600,000 and infer 100,000 of interest, but the true interest is closer to 101,755 precisely because of that extra fractional month. The years figure is more intuitive for planning — about 4.18 years tells you the loan straddles a little past the four-year mark — but it hides the partial-payment detail. When you compare scenarios, watch the month count rather than the rounded years, because small payment changes often shift the term by a few months without visibly moving the years. A good habit is to treat the months output as the exact answer and the years output as a readable summary. If you need a debt-free date, count the months forward from your next payment, then add one more month to account for the fractional final payment that the formula almost always produces.
Why a fixed rate matters for the result
Every number this calculator produces rests on one assumption: the interest rate stays fixed for the entire payoff period. That holds neatly for fixed-rate installment loans, where the rate is locked at origination and the monthly interest charge depends only on the shrinking balance. For variable-rate debt the picture is different. If your rate can move, the monthly interest charge will rise or fall with it, which changes how much of each fixed payment reaches principal and therefore changes the payoff timeline. A rate increase means more of your payment is consumed by interest, pushing the finish line out; a rate cut does the opposite. The calculator cannot foresee those moves, so on variable debt the honest approach is to treat each result as a snapshot under today's rate and re-run it whenever the rate resets. You can also stress-test a variable loan by entering a higher rate than your current one to see how much the timeline could stretch in an adverse scenario, then size your payment with that cushion in mind. The same caution applies to loans with introductory teaser rates that later step up. For fixed-rate loans none of this applies — the timeline the tool reports is the timeline you will actually experience, provided you hold the payment steady. Knowing which kind of loan you hold tells you how much to trust a single run of the numbers.
Building a practical payoff plan
Turning these mechanics into a plan starts with finding the largest payment you can sustain without straining the rest of your budget, because the payoff math rewards consistency far more than occasional heroics. Begin by clearing the interest-floor with real margin: a payment only a little above the monthly interest charge leaves you decades from freedom, so aim well past it. From there, test round payment levels in the calculator and watch how the term and total interest respond — you will usually find a sweet spot where a modest increase buys a large reduction in interest before the gains start to flatten. Lock in that payment and automate it so the plan runs without monthly willpower. When extra money arrives — a bonus, a refund, the end of another obligation — route it to the balance as a lump and re-run the numbers to see the timeline jump forward. Revisit the calculation whenever your balance, rate, or budget changes, since each run gives you an updated debt-free date to aim at. Keep the comparison honest by tracking total interest, not just the monthly payment: a plan that feels comfortable but stretches the term can quietly cost far more over its life. The discipline is simple — pay as much as you reliably can, attack principal early, and let the reverse-compounding of a shrinking balance do the heavy lifting. The calculator's job is to make each of those choices visible before you commit to them.
Frequently asked questions
Why does the calculator say my payment is too low?
Because your payment is at or below the first month's interest charge — balance times the monthly rate. With the default 500,000 balance at 9%, that floor is 3,750. A payment at or under it is entirely consumed by interest, so the balance never falls and there is no finite payoff time. Raise the payment above the floor and a timeline appears.
How much does paying a little more each month actually help?
More than you might expect, because the effect is non-linear. On the default loan, 12,000 a month clears it in about 50 months with roughly 101,755 of interest, but 6,000 a month takes about 131 months and costs about 287,602. Every extra unit shrinks the balance that future interest is charged on, so the savings compound across the whole remaining term.
What happens if I make a single large extra payment?
Subtract the lump from your current balance and re-run the numbers at your usual payment. Paying a one-off 50,000 on the default loan drops the balance to 450,000; at 12,000 a month it then clears in about 44 months instead of 50, cutting interest from about 101,755 to about 80,366 — a saving near 21,389. The earlier the lump lands, the more it saves.
Does this assume a fixed interest rate?
Yes. The calculation assumes the rate stays constant for the whole payoff period, which is true for fixed-rate loans. For variable-rate debt, treat the result as a snapshot under today's rate and re-run it whenever the rate changes, since a higher rate leaves less of each payment for principal and lengthens the timeline.
Why is the payoff time shown as a fraction of a month?
The formula rarely produces a whole number. The default works out to about 50.15 months, meaning the loan is gone after 50 full payments plus a small partial payment in the following month. That fractional tail is also why multiplying a rounded 50 months by the payment understates the true interest — use the precise month count for accurate totals.
Is total interest or the monthly payment the better thing to watch?
Track total interest. A comfortable-looking payment that stretches the term can quietly cost far more over the life of the loan than a slightly higher payment that finishes sooner. The monthly payment tells you affordability; total interest tells you the real price of the plan.