To calculate your credit card payoff, you need three numbers: your current balance, your annual percentage rate (APR), and the monthly payment you plan to make. With those inputs, you can figure out exactly how many months it will take to reach a zero balance and how much total interest you’ll pay along the way. The math involves a specific formula, but understanding the logic behind it is just as important as plugging in numbers.
The Core Payoff Formula
Credit card interest compounds, meaning you’re charged interest on previously accumulated interest. That’s what makes payoff timelines feel so stubbornly long. The standard formula for calculating the number of months to pay off a balance is:
Months = −log(1 − (balance × r / payment)) / log(1 + r)
In this formula, “r” is your monthly interest rate, which you get by dividing your APR by 12. So if your APR is 19.16% (the current average as of early 2026), your monthly rate is 0.1916 / 12 = 0.01597, or about 1.6%.
Here’s a concrete example. Say you owe $5,000 at a 20% APR and you commit to paying $200 per month. Your monthly rate is 0.20 / 12 = 0.01667. Plug those in:
- balance × r / payment = 5,000 × 0.01667 / 200 = 0.4167
- 1 − 0.4167 = 0.5833
- −log(0.5833) / log(1.01667) = 0.2341 / 0.007153 = about 32.6 months
Round up to 33 months. Over that time, you’d pay roughly $6,500 total, meaning about $1,500 goes to interest alone on that $5,000 balance. That’s 30% extra on top of what you originally charged.
How Your Interest Actually Accumulates
Most issuers calculate interest using the average daily balance method. Each day of your billing cycle, the bank records what you owe. It adds new purchases and subtracts payments as they post, then averages all those daily snapshots together. The formula looks like this:
Monthly interest = average daily balance × daily periodic rate × number of days in the billing cycle
Your daily periodic rate is your APR divided by 365. At a 20% APR, that’s about 0.0548% per day. On a $5,000 balance over a 30-day cycle, that comes to roughly $82 in interest for the month. Some issuers use a compounding version of this method where each day’s interest gets added to the balance before calculating the next day’s charge. The difference is small over a single month but adds up over years.
This is why large balances feel like they barely shrink. At 20% APR, a $5,000 balance generates about $82 in interest per month. If your minimum payment is only $100, just $18 actually reduces what you owe.
Why Minimum Payments Stretch the Timeline
Minimum payments are designed to keep your account current, not to pay off your debt efficiently. Large issuers typically calculate them as 1% of your balance plus all interest and fees charged that cycle. Some issuers, particularly credit unions, use a flat 2% of the statement balance instead. Either way, every card has a floor amount, often $25 or $40, that kicks in when the calculated minimum would be lower than that threshold. If your total balance is less than the floor, your minimum is simply the full amount owed.
The problem is clear when you run the numbers. On that $5,000 balance at 20% APR, a 1%-plus-interest minimum payment starts around $133 in month one. That sounds reasonable, but it drops every month as the balance shrinks, so you’re always paying just barely more than the interest charge. Paying only the minimum on a $5,000 balance can stretch repayment past 15 years and cost thousands in interest.
Your credit card statement actually spells this out. Federal law requires issuers to print a “Minimum Payment Warning” box on every statement showing how long it will take to pay off your current balance making only minimum payments, along with the total dollar cost. It also shows the fixed monthly payment needed to eliminate the balance in three years. Comparing those two numbers is one of the fastest ways to see the real cost of minimums.
A Step-by-Step Payoff Calculation
If you want to work through the math month by month rather than using the logarithmic formula, here’s how to do it by hand or in a spreadsheet:
- Step 1: Write down your starting balance, APR, and the fixed monthly payment you’ll make.
- Step 2: Calculate one month’s interest. Multiply the balance by your APR, then divide by 12. For $5,000 at 20% APR: $5,000 × 0.20 / 12 = $83.33.
- Step 3: Add the interest to the balance: $5,000 + $83.33 = $5,083.33.
- Step 4: Subtract your payment: $5,083.33 − $200 = $4,883.33. That’s your new balance entering month two.
- Step 5: Repeat. Each month the interest charge shrinks because the balance is a little smaller, so a larger share of your payment goes toward principal.
Keep going until the balance hits zero. Tally up all the interest charges from each row, and you have your total interest cost. This month-by-month approach is slightly less precise than the daily balance method your issuer uses, but it’s close enough to plan around and easy to build in any spreadsheet.
How to Calculate a Target Payoff Date
If you want to be debt-free by a specific date, work the formula in reverse. Decide how many months you have, then solve for the payment. The formula is:
Payment = balance × r × (1 + r)^n / ((1 + r)^n − 1)
Here, “r” is still your monthly rate (APR / 12), and “n” is the number of months. Want to pay off $5,000 at 20% APR in 12 months? Your monthly rate is 0.01667, and n is 12. The result is about $463 per month. You’d pay roughly $5,556 total, with $556 going to interest. Compare that to the 33-month plan at $200/month, where you’d pay $1,500 in interest. Cutting the timeline by 21 months saves nearly $1,000.
What Changes the Numbers Most
Three levers control your payoff timeline, and they’re not equally powerful.
Payment amount has the biggest impact. Even $50 extra per month can shave years off a large balance. On a $5,000 debt at 20% APR, bumping your payment from $150 to $200 cuts the payoff time from about 47 months to 33 months and saves roughly $900 in interest.
Interest rate matters more than most people expect. The average credit card APR is 19.16% as of April 2026, but rates range from about 11.5% to 32.5% depending on the card and your credit profile. That same $5,000 balance with $200 monthly payments takes 28 months at 12% APR versus 38 months at 28% APR. The high-rate borrower pays nearly $1,500 more in interest. If you qualify for a lower-rate card or a balance transfer offer, recalculating with the new rate will show you exactly how much you’d save.
New charges are the hidden variable. Every payoff calculation assumes you stop adding to the balance. A single $500 purchase mid-payoff doesn’t just add $500 to the timeline. It adds $500 plus all the interest that $500 will generate over the remaining months. If you’re serious about a payoff plan, stop using the card or at least pay new charges in full each month so they don’t enter the interest cycle.
Using Your Statement’s Built-In Numbers
Before building a spreadsheet, check the payoff disclosure box on your latest statement. It shows the estimated months (or years) to pay off your current balance at the minimum payment, the total cost including interest, and the monthly payment needed to clear the balance in three years. These figures are calculated by your issuer using your actual APR and current balance, so they’re precise starting points.
If the three-year payment fits your budget, that’s a solid baseline. If it doesn’t, use the formulas above to find a payment amount and timeline that works for you. Even paying $10 or $20 more than the minimum each month will meaningfully reduce your total interest cost, because that entire extra amount goes straight toward reducing the balance rather than covering interest.