How long will it take to pay off my credit card debt?

Divide the balance by what you can pay, then correct for interest — the page does the correction for you. On 20,000 at 12% paying 750 a month, the answer is 32 months and 3,378.27 in interest. The same balance paying 500 takes 52 months and costs 5,669.33. The important condition is that you stop adding to the card; the answer describes a balance you are only paying down.

Why does the calculator say my payment is too low?

Because it is at or below the interest the balance earns in a month, so the debt never gets smaller. On 20,000 at 12%, that threshold is 200 a month. Pay exactly 200 and the balance stays the same forever; pay less and it grows. Anything above it works, but the closer the payment is to the threshold, the longer the payoff time becomes.

Why is the total paid not the monthly payment times the number of months?

Because the last payment is whatever is left rather than a full one. On 20,000 at 12% paying 750, thirty-one payments of 750 leave 128.27, so the final payment is 128.27 and the total is 31 × 750 + 128.27 = 23,378.27. The page reports that final payment as its own figure so the arithmetic can be checked.

How much difference does paying a bit more each month make?

More than proportionally. On 20,000 at 12%, paying 750 instead of 500 cuts the payoff time from 52 months to 32 and the interest from 5,669.33 to 3,378.27 — a third more each month for 40% less interest. The effect is strongest when the payment is only just above the monthly interest, because that is where the balance is barely falling and almost everything you pay is interest.

Does this work for a mortgage or a car loan?

The arithmetic does — it is the same formula used backwards — but those loans have a fixed term and a payment set by the lender, so the useful direction is the other one: enter the amount, the rate and the term to get the payment. This page is for the case where you choose the payment: credit cards, personal loans you want cleared early, and money owed to a person rather than an institution.

What does the final payment figure tell me?

It tells you how much of the last month is a real payment and how much is just the rounding. Clearing 20,000 at 12% with 750 a month leaves 128.27 for the last month; at 0% with 500 a month it leaves exactly 500, so the final payment is a full one. Either way, the balance reaches zero in that month — the loan does not run on for another full payment.

Loan Repayment Calculator

Result

Months to clear the balance

The same, in years: 2.7
Total interest: 3,378.27
Total paid: 23,378.27
Final payment: 128.27

A loan repayment calculator that answers the other half of the question. The rest of this category takes a term and returns a payment; this page takes a payment and returns the term, which is what you actually know when you are clearing a balance rather than taking out a loan. Enter what you owe, the annual interest rate and the amount you can put towards it each month, and the page returns how many months it takes to clear, the same figure in years, the total interest you pay along the way, the total you hand over, and the size of the final payment. That last figure matters more than it looks: the last payment is whatever is left rather than a full one, so on the default loan — 20,000 at 12% paying 750 a month — the answer is 32 months, and the last of those payments is 128.27. The relationship between the payment and the term is not a straight line, which is the thing this page exists to show: paying 500 a month instead of 750 takes 52 months rather than 32 and costs 5,669.33 in interest rather than 3,378.27. Raising the payment by a half cuts the interest by more than a third. Credit card debt, a personal loan you want gone early and a family loan you are repaying all come out of the same arithmetic.

20,000 at 12%, by monthly payment

Monthly payment	Months to clear	Total interest	Total paid
500	52	5669.33	25669.33
750	32	3378.27	23378.27
1000	23	2426.96	22426.96
1500	15	1574.03	21574.03

Every row is the same balance — 20,000 at 12%, which is this page's default — and only the monthly payment changes. Read the first column against the third: tripling the payment from 500 to 1,500 cuts the months from 52 to 15, and cuts the interest from 5,669.33 to 1,574.03 — a saving of 4,095.30, which is far more than the extra 1,000 a month costs over fifteen months. That is the point of the table: the payment and the interest do not move together, and the money spent clearing a balance early buys more than the same money spent later. Your own balance will sit elsewhere, so use the calculator above rather than reading across.

Formula

n = −ln(1 − P × r ÷ A) ÷ ln(1 + r), where n is the number of payments, rounded up to the next whole month

P: The amount you owe when you start
r: Monthly interest rate: the annual rate divided by twelve
A: What you pay each month
n: Number of payments needed to clear the balance, rounded up
yr: The same answer in years: the number of months divided by twelve

Use it whenever the payment is the thing you control and the term is the unknown — clearing a credit card, paying off a personal loan early, or working out what a larger monthly amount would buy you. Start with what you can genuinely afford every month and look at the interest figure rather than the term: the number of months falls steadily as the payment rises, but the interest falls faster, and the last stretch is where most of the saving is. Then try a slightly higher payment and compare the two interest totals; the gap between them is what that extra money is worth over the life of the debt. If the answer comes back as hundreds of months, the payment is barely covering the interest and the page will say so rather than print a number you cannot act on.

Worked examples

20,000 at 12%, paying 750 a month
1. Monthly rate: 12 ÷ 12 = 1% a month, which is 0.01 as a decimal
2. Number of payments: −ln(1 − 20,000 × 0.01 ÷ 750) ÷ ln(1.01) = 31.0, rounded up to 32
3. Thirty-one full payments of 750 leave 128.27 outstanding, so the last payment is 128.27
4. Total paid: 31 × 750 + 128.27 = 23,378.27
5. Total interest: 23,378.27 − 20,000 = 3,378.27
6. In years: 32 ÷ 12 = 2.7
This is the page's default and the balance behind the reference chart below. Note that 32 × 750 is 24,000, but the total paid is 23,378.27 — the last payment is a partial one, which is why the total is not the payment multiplied by the term.
The same 20,000 at 12%, paying 500 a month
1. First month's interest: 20,000 × 0.01 = 200.00, so the first payment clears 300 of the balance
2. Number of payments: −ln(1 − 20,000 × 0.01 ÷ 500) ÷ ln(1.01) = 51.3, rounded up to 52
3. Total paid: 51 × 500 + 169.33 = 25,669.33
4. Total interest: 25,669.33 − 20,000 = 5,669.33 — 2,291.06 more than paying 750
A third less each month: the term stretches from 32 months to 52, and the interest rises by 68%. The payment fell by a third and the cost rose by more than two thirds, which is the asymmetry this whole page is about.
20,000 at 0%, paying 500 a month
1. Zero rate: nothing accrues, so the whole of each payment reduces the balance
2. Number of payments: 20,000 ÷ 500 = 40 exactly, and no rounding up is needed
3. Total paid: 40 × 500 = 20,000 — exactly the amount owed
4. Total interest: 0
5. Final payment: 500, a full one, because the division came out even
At zero the answer is just the balance divided by the payment, and the last payment is a full one because nothing was left over. Every other case on this page has a final payment smaller than the rest.

Limitations

The monthly payment has to be larger than the first month's interest, or there is no answer at all: if you owe 20,000 at 12%, the first month costs 200 in interest, and a payment of 200 or less leaves the balance exactly where it was or growing. The page reports that rather than returning a number, because the mathematically correct answer is an infinite term and a figure like that on screen is worse than an explanation. There is also an upper limit of one hundred years of payments, which the page treats as a sign that the payment is too small to be worth calculating. Three things the arithmetic assumes. It assumes you add nothing new to the balance — a credit card you keep spending on never pays off, however faithfully you make the payment, and the answer here only describes a card you have stopped using. It assumes a fixed rate for the whole period, which a variable-rate card does not have. And it assumes the payment stays the same every month; a card's minimum payment is usually a percentage of the balance that shrinks as the balance falls, which stretches the payoff far beyond what this page returns. Fees, late charges and any interest-free period at the start are not modelled, and the amounts carry no currency symbol — they are right in whatever currency you typed them in and meaningless in any other.

Frequently asked questions

How long will it take to pay off my credit card debt?: Divide the balance by what you can pay, then correct for interest — the page does the correction for you. On 20,000 at 12% paying 750 a month, the answer is 32 months and 3,378.27 in interest. The same balance paying 500 takes 52 months and costs 5,669.33. The important condition is that you stop adding to the card; the answer describes a balance you are only paying down.
Why does the calculator say my payment is too low?: Because it is at or below the interest the balance earns in a month, so the debt never gets smaller. On 20,000 at 12%, that threshold is 200 a month. Pay exactly 200 and the balance stays the same forever; pay less and it grows. Anything above it works, but the closer the payment is to the threshold, the longer the payoff time becomes.
Why is the total paid not the monthly payment times the number of months?: Because the last payment is whatever is left rather than a full one. On 20,000 at 12% paying 750, thirty-one payments of 750 leave 128.27, so the final payment is 128.27 and the total is 31 × 750 + 128.27 = 23,378.27. The page reports that final payment as its own figure so the arithmetic can be checked.
How much difference does paying a bit more each month make?: More than proportionally. On 20,000 at 12%, paying 750 instead of 500 cuts the payoff time from 52 months to 32 and the interest from 5,669.33 to 3,378.27 — a third more each month for 40% less interest. The effect is strongest when the payment is only just above the monthly interest, because that is where the balance is barely falling and almost everything you pay is interest.
Does this work for a mortgage or a car loan?: The arithmetic does — it is the same formula used backwards — but those loans have a fixed term and a payment set by the lender, so the useful direction is the other one: enter the amount, the rate and the term to get the payment. This page is for the case where you choose the payment: credit cards, personal loans you want cleared early, and money owed to a person rather than an institution.
What does the final payment figure tell me?: It tells you how much of the last month is a real payment and how much is just the rounding. Clearing 20,000 at 12% with 750 a month leaves 128.27 for the last month; at 0% with 500 a month it leaves exactly 500, so the final payment is a full one. Either way, the balance reaches zero in that month — the loan does not run on for another full payment.

References

Compound Interest Calculator — why a balance that barely falls keeps costing interest month after month — U.S. Securities and Exchange Commission (Investor.gov)
Consumer Credit — G.19 — the interest rates actually charged on credit cards and other consumer debt — Board of Governors of the Federal Reserve System (United States)

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