Loan Payoff Calculator

How this is calculated

This solves the amortisation formula for TIME rather than for the payment. Given a balance B, a monthly rate r and a payment P, the number of months is the negative logarithm of (1 minus r times B over P), divided by the logarithm of (1 plus r). The monthly rate is the annual rate divided by 12 and then by 100 - so 18 percent annual is 0.015 per month. Both conversions are inside the formula rather than described beside it, because a formula and its glossary drift apart. ⚠️ THERE IS A PAYMENT BELOW WHICH THE LOAN NEVER CLEARS, and it is the most important number here. Each month the balance grows by the interest charged and shrinks by your payment. If the payment is smaller than the interest, the balance grows - forever. That threshold is simply the balance times the monthly rate. On a 5,000 dollar balance at 18 percent, the interest alone is 75 dollars a month. Pay 75 and you will pay 75 dollars a month for the rest of your life and still owe 5,000. Pay 76 and it clears, eventually - in 291 months, which is 24 years, and costs 17,107 dollars in interest on a 5,000 dollar debt. The calculator returns a dash rather than a number when the payment cannot clear the debt, because any number there would be a lie. That is what a minimum payment on a credit card is doing. It is set as a percentage of the balance and it is deliberately just above this threshold, which is why paying only the minimum takes decades. EXTRA PAYMENTS ARE WORTH FAR MORE THAN THEY LOOK, because every dollar above the interest goes straight against principal, and then never accrues interest again. The tool shows what an extra amount does to both the time and the total, and the effect is usually startling - especially early, when the balance is largest. The reason is that this is a logarithm, not a straight line. Doubling your payment does not halve the time; it cuts it by considerably more. ⚠️ THIS ASSUMES A FIXED RATE AND NO NEW BORROWING. On a credit card, both of those are usually false. Continuing to spend on the card while paying it down is the commonest reason a payoff plan quietly fails, and the arithmetic here cannot see it. Rates on cards are also variable and can change. CHECK FOR EARLY REPAYMENT CHARGES on any fixed-term loan before overpaying. Some lenders penalise exactly the behaviour this calculator recommends.

Common questions

Why does it sometimes show a dash?

Because that payment will never clear the debt, and any number there would be a lie. Each month the balance grows by the interest charged and falls by your payment - so if the payment is smaller than the interest, the balance grows forever. The threshold is the balance times the monthly rate, shown as its own output. On 5,000 dollars at 18 percent that is 75 dollars a month: pay exactly 75 and you will still owe 5,000 in thirty years.

Is that what a credit card minimum payment is?

Effectively, yes. A card minimum is typically set as a small percentage of the balance, calculated to sit just above the interest-only threshold. That is precisely why paying only the minimum takes decades and costs enormously - it is designed to clear the debt, eventually, while maximising the time it takes. Seeing the interest-only figure next to your actual payment is the fastest way to understand what a minimum payment really is.

Why does a small extra payment help so much?

Two reasons compound. First, every dollar above the interest goes STRAIGHT against principal - and that principal then never accrues interest again, for the whole remaining life of the loan. Second, the relationship between payment and time is logarithmic rather than linear, so doubling the payment cuts the time by considerably more than half. The saving is largest early, when the balance is biggest, which is why acting now beats acting later by more than the delay suggests.

What does the total interest tell me?

The price of the time. It is the difference between everything you pay and what you borrowed, and on a high-rate debt paid slowly it can approach or exceed the original balance. It is worth looking at once as a single number, because a monthly payment is designed to feel manageable and a total is designed by nobody - which is exactly why the total is the more honest figure.

Does this work for a credit card?

The arithmetic does, with two caveats that matter. It assumes a FIXED rate, and card rates are variable. And it assumes NO NEW BORROWING - continuing to spend on the card while paying it down is the commonest reason a payoff plan quietly fails, and nothing here can see it. Treat the answer as what happens if you stop using the card today, which is also the plan most likely to work.

Should I always overpay?

Usually, on high-rate debt - but check for early repayment charges first, because some fixed-term loans penalise exactly this. It is also worth comparing against other uses of the money: paying off an 18 percent debt is a guaranteed 18 percent return, which beats almost anything else available, while overpaying a low-rate loan may not beat keeping an emergency fund. The rate is what decides it, and this calculator will show you the saving so you can compare properly.

Take it further with AI

Copy this into ChatGPT or Claude with your own numbers filled in. It hands over the figures this calculator worked out, so the answer is built on real arithmetic instead of a guess.

I used the Loan Payoff Calculator at https://www.bfcbrilliance.com/tools/loan-payoff-calculator.

What I entered:
- Balance owed ($): ___
- Annual interest rate (%): ___
- Monthly payment ($): ___
- Extra per month, if you could ($): ___

What it calculated:
- Months to clear it: ___
- Payment that only covers interest: ___
- In years: ___
- Total you will pay: ___
- — of which interest: ___

Use those figures as given — they are already worked out, so please don't recalculate or estimate your own. Help me turn them into a plan: what to buy or do, in what order, roughly what it should cost, and the mistakes people most often make with this job.

Keep this general and do not give financial advice — flag where I should talk to a qualified adviser.

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