Credit Card Payoff Formula: Months, Payment and Interest
The credit card payoff formula is n = −ln(1 − B × i ÷ P) ÷ ln(1 + i). Here n is the number of months, B is your balance, i is your monthly rate (APR ÷ 12) and P is your fixed monthly payment. Run the formula in reverse and you get the payment needed to be debt-free by a date you choose. Below you will find both versions, worked on a $5,000 balance, plus the places where real cards drift away from the math.
TL;DR
- Months to pay off = −ln(1 − B × i ÷ P) ÷ ln(1 + i), with i = APR ÷ 12. It only works if P is bigger than B × i, the interest that accrues in one month.
- Payment needed to finish in n months = B × i ÷ (1 − (1 + i)^−n).
- On $5,000 at 22% APR, $200 a month takes about 34 months and roughly $1,750 in interest. Paying $300 takes 21 months and roughly $1,022.
- Real cards add daily balance methods, fees and promotional rates, so treat the result as a close estimate, not a payoff quote.
- With several cards, keep paying every minimum and send the extra to the highest APR.
Table of Contents
- The formula in plain terms
- How many months to pay off a credit card
- What monthly payment clears $5,000 by a set date
- Where the formula and your statement disagree
- Do it in a spreadsheet
- Paying off more than one card
- Perspective: why we trust the estimate, and where we stop trusting it
- Run your numbers on MetriqaHub
- Common mistakes to avoid
- FAQ
- Sources
The formula in plain terms
The simple-interest formula many people meet first is I = P × R × T: interest equals principal times rate times time. The Consumer Financial Protection Bureau teaches it in its credit card payment lesson, and says outright that it oversimplifies how card interest really works. It is a useful first look, but it cannot tell you how long a balance lasts. That is because every payment shrinks the balance, so next month's interest is smaller than this month's.
A payoff formula handles this by treating the card like an amortizing loan with a fixed payment. Four inputs drive it:
| Symbol | Meaning | Where to find it |
|---|---|---|
| B | Current balance | Your latest statement or card app |
| APR | Annual percentage rate, the yearly cost of borrowing as a percentage | Statement, in the interest charges section |
| i | Monthly rate = APR ÷ 12, written as a decimal | You calculate it |
| P | Fixed monthly payment you plan to make | Your choice |
To get i, divide the APR by 12 and then by 100. A 22% APR becomes 22 ÷ 12 = 1.8333% a month, or 0.018333 as a decimal.
How many months to pay off a credit card
The question "how long will this take" has a clean answer when your payment stays fixed and you stop adding new charges:
n = −ln(1 − (B × i) ÷ P) ÷ ln(1 + i)ln is the natural logarithm, a button on any scientific calculator and a function in every spreadsheet (=LN()).
Worked example: $5,000 at 22% APR, $200 a month
- Monthly rate: i = 0.22 ÷ 12 = 0.018333.
- First month's interest: B × i = 5,000 × 0.018333 = $91.67.
- Divide by the payment: 91.67 ÷ 200 = 0.4583.
- Subtract from 1: 1 − 0.4583 = 0.5417.
- Take the natural log: ln(0.5417) = −0.6131.
- Denominator: ln(1.018333) = 0.018167.
- Months: 0.6131 ÷ 0.018167 = 33.75, so 34 payments, the last one smaller.
The one condition that matters
Look at step 3. If your payment is no larger than B × i, the number inside the log becomes zero or negative and the formula fails. That is not a glitch. It means the payment only covers interest, so the balance never falls. On $5,000 at 22%, any payment of $91.67 or less leaves you where you started.
What changing the payment does
Same card, same rate, different payments:
| Monthly payment | Months to pay off | Approx. total interest |
|---|---|---|
| $150 | 52 | $2,798 |
| $200 | 34 | $1,750 |
| $300 | 21 | $1,022 |
Official examples show the same pattern. Canada's consumer agency shows that a $2,000 balance at 18% takes 3 years 11 months and $793 in interest at $60 a month, against 1 year 2 months and $231 at $160. In the U.S., MyCreditUnion.gov models a $1,500 balance at 19%: a minimum of 4% of the balance starts at $60, takes 106 payments and costs more than $889 in interest, while a 2.5% minimum starts at $37.50, takes 208 payments and costs more than $2,138. Both assume no new charges or late fees.
What monthly payment clears $5,000 by a set date
Sometimes you start from a deadline: a wedding, a move, the end of a 0% offer. Solve the same equation for P:
P = B × i ÷ (1 − (1 + i)^−n)Here n is the number of months you give yourself.
Worked example: $5,000 at 22% APR in 24 months
- B × i = $91.67.
- (1.018333)^24 = 1.5467, so (1.018333)^−24 = 0.6465.
- 1 − 0.6465 = 0.3535.
- P = 91.67 ÷ 0.3535 = about $259.39.
Three deadlines compared
| Payoff target | Monthly payment | Approx. total interest |
|---|---|---|
| 12 months | $467.97 | $616 |
| 24 months | $259.39 | $1,225 |
| 36 months | $190.95 | $1,874 |
Where the formula and your statement disagree
The formulas assume one rate, one balance, a fixed payment, and no new spending. Real cards bend each of those.
Daily balance interest. Many issuers compute interest on an average daily balance. A University of Kentucky Extension guide shows the method: a $301.61 average daily balance times a 1.8% monthly rate gives a $5.43 finance charge. Because interest accrues daily, the exact dollar amount differs slightly from APR ÷ 12. Our credit card interest formula guide walks through the daily version step by step. Several balances on one card. A Federal Reserve sample credit card disclosure.pdf) lists purchase, balance transfer and cash advance rates, penalty APRs and fees as separate items. A single-APR formula cannot see these. If your card has a promotional balance at 0% and a regular balance at 24%, calculate them as separate pieces. Minimum payments that move. A fixed-payment formula is not a minimum-payment formula. Minimums usually shrink as the balance falls, which stretches the payoff. A cardmember agreement on file with the CFPB shows minimums built from a percentage of the balance plus interest, past-due amounts and fees, and the exact recipe depends on the issuer. To use the formula honestly, pick a payment at or above your first minimum and hold it constant. Statement balance versus payoff balance. The number on the statement is not always what it takes to close the account today, because interest keeps accruing between the statement date and the payment date. The same idea applies to any loan, as payoff quotes explained shows for title loans: the balance on a bill and the true payoff figure are two different numbers. For a final payment, ask the issuer for the current payoff amount.Do it in a spreadsheet
You do not need to do logarithms by hand. In Excel or Google Sheets, put the balance in A1, the APR as a decimal in A2 (0.22) and the payment in A3:
- Months to pay off:
=NPER(A2/12, -A3, A1) - Payment for a target of 24 months:
=PMT(A2/12, 24, -A1)
These built-in functions use the same math as the formulas above. NPER returns a fractional number, so round up for the number of payments. For a visual check, build a table with one row per month: opening balance, interest (balance × i), payment, closing balance. Stop when the closing balance reaches zero.
Paying off more than one card
The formula is a single-card tool. With several cards, the question becomes which one gets the extra dollars. The St. Louis Fed compared strategies and found that paying minimums on every account and putting extra money on the highest-rate card cost the least interest and finished one to three months sooner than the alternatives it tested.
A practical routine:
- List each card's balance, APR and minimum.
- Decide one total monthly amount for all cards.
- Pay each minimum, and send everything left over to the highest APR.
- When that card hits zero, roll its whole payment onto the next-highest APR.
- Recalculate with the formula after each card closes out.
Paying the smallest balance first can feel better, and if motivation is what keeps you paying, that has real value. Just know the cost: you will usually pay more interest than with the highest-rate-first order.
Perspective: why we trust the estimate, and where we stop trusting it
We build calculators for a living, and the most common mistake we see is false precision. A payoff formula gives you a clean number, 33.75 months or $259.39, and people treat it as a promise. It is a model. Its strength is that it makes trade-offs visible: you can see in seconds that $100 more a month saves a year, or that a payment barely above the monthly interest is a treadmill.
We suggest using it for decisions, not for the last dollar. Decide the payment, check it against the formula, then compare with your first real statement after you start. If the statement shows more interest than expected, look for fees, a second balance at a higher rate, or new purchases. The gap is usually explained by one of those.
The same logic applies when you consider moving a balance to a cheaper card. The fee and the new rate should be compared with the interest you would otherwise pay, much like a refinance break-even calculation.
— Nkosi
Run your numbers on MetriqaHub
If you would rather skip the logs, our free finance calculators on MetriqaHub give instant results with no registration. Enter a balance, rate and payment, and you get your payoff time and interest. Once the card is gone, point the same monthly amount at a goal with our savings goal formula and examples.
Common mistakes to avoid
- Using APR as the monthly rate. Divide by 12 first. Plugging 22% in as 0.22 per month overstates interest by a factor of 12.
- Forgetting new charges. The formula assumes the balance only falls. If you keep using the card, the real payoff date moves out.
- Assuming the minimum stays flat. Minimums drop as the balance drops. Lock in a fixed payment to beat the schedule.
- Ignoring a payment at or below monthly interest. Check B × i first. If your payment does not beat it, nothing is being paid down.
- Mixing rates. If a card has promotional and standard balances, model each separately.
FAQ
How do I calculate months to pay off a credit card?
Use n = −ln(1 − B × i ÷ P) ÷ ln(1 + i), where B is the balance, i is APR ÷ 12 as a decimal and P is your fixed monthly payment. In a spreadsheet, =NPER(APR/12, -payment, balance) does the same thing. Round the result up to get the number of payments.
What is the debt payoff formula for a fixed payment?
Solving for the payment gives P = B × i ÷ (1 − (1 + i)^−n). It is the standard amortizing loan payment formula applied to a card with no new charges. For $5,000 at 22% over 24 months it returns about $259.39.
Why does my statement show more interest than the formula?
Cards often compute interest on an average daily balance, and they may charge different rates on purchases, transfers and cash advances. Fees and new purchases add to the total as well. The formula is a good estimate for planning, but your statement is the final word.
Should I pay the highest-rate card or the smallest balance first?
Paying minimums on all cards and sending extra money to the highest APR costs the least interest, as the St. Louis Fed's comparison found. The smallest-balance-first order can help if you need quick wins to stay motivated, but it typically costs more.
Sources
- CFPB: Managing credit card payments
- Financial Consumer Agency of Canada: Paying off your credit card
- MyCreditUnion.gov: Paying Off Credit Cards
- University of Kentucky Extension: How Finance Charges Are Calculated on Credit Cards
- Federal Reserve: Sample credit card disclosure.pdf)
- CFPB database: Citi Double Cash cardmember agreement
- St. Louis Fed: Best strategy for paying off credit card debt
- Title loan payoff quotes explained