How this instrument works
A standard loan calculator fixes the number of payments and solves for the payment amount. This instrument runs that identity backward: it fixes the payment you choose to make and solves for how many months that payment takes to clear a revolving balance. The rearrangement pulls a natural logarithm out of the compounding equation, because inverting an exponential for its exponent is what a logarithm does — the log isn't decoration, it is the only way to isolate months when payment and rate are already fixed.
That reversal matters because a credit card, unlike a mortgage or an auto loan, never told you how many payments it would take in the first place. The card only sets a minimum, and the minimum keeps shrinking as the balance falls, so the true payoff date stays hidden inside a moving target. Choosing a fixed dollar amount instead — the same $200, say, every single month — turns a revolving debt into something with an actual, calculable end date, which is the number this page returns.
The formula assumes the payment stays exactly level, the APR never moves, and no new purchase touches the card before it's paid off. Real cards drift from all three: a promotional rate expires, a payment gets skipped, a purchase lands mid-payoff. Each of those resets the clock and calls for a fresh run of the same math, not a patch to this one — the instrument is honest about the schedule for the payment plan as entered, nothing more.
- Enter what the card currently owes in Current balance, $.
- Enter the card's annual rate in APR, % — read it straight off your statement, not an introductory teaser rate that has already expired.
- Enter the flat amount you plan to pay every month in Fixed monthly payment, $ — your own chosen figure, not the card's shifting minimum.
- Read Months to pay off — the exact month the balance reaches zero at that payment, held level the whole way.
- Raise or lower the payment and re-run it to see how many months a change actually buys or costs.
Worked example — $5,000 at 22% APR, $200 a month
Feed a $5,000 balance, a 22% APR, and a fixed $200 monthly payment into the formula. The monthly rate r works out to 0.018333 (22 ÷ 100 ÷ 12), rB ⁄ PMT comes to 0.458333, and n = −ln(0.541667) ⁄ ln(1.018333) returns 33.7476861944 months — a little under two years and ten months of steady $200 payments before the balance reaches zero.
Multiply that 33.7476861944 by the $200 payment and the card absorbs $6,749.54 in total payments to erase a $5,000 balance — $1,749.54 of it interest, the price of clearing debt at a fixed monthly amount instead of a lump sum.
Raise the same $5,000 balance's payment to $1,000 a month and the identical formula returns 5.29213695046 months. Nearly quintupling the payment cuts the payoff time to a sixth of what it was, because most of the smaller $200 payment was servicing interest rather than reaching principal in the first place.
Questions
Why does the payoff formula involve a natural log?
Because solving compound interest for time rather than for payment means inverting an exponential, and a logarithm is what undoes an exponent. The usual loan formula fixes the number of months and solves for the payment; this instrument fixes the payment and solves for months, which requires rearranging the compounding equation into exactly this log form.
What happens if my payment barely covers the interest?
The payoff time stretches enormously. On a $5,000 balance at 22% APR, monthly interest alone runs about $91.67; paying $91.67 a month returns 562.657930516 months — nearly 47 years — because almost the entire payment is consumed by interest before any of it reaches principal. Drop the payment below that interest floor and the balance never shrinks at all.
How much difference does raising the payment actually make?
A lot, because interest claims a roughly fixed dollar amount each month no matter the payment size. Raising a $5,000, 22% APR balance's payment from $200 to $1,000 a month cuts payoff time from 33.7476861944 months to 5.29213695046 months, since the smaller payment was spending most of itself on interest rather than principal.
Is the payment I enter the same as my card's minimum payment?
No. Issuers typically set a minimum as the greater of a flat dollar floor or roughly 1% to 3% of the balance plus that month's interest, and the minimum keeps shrinking every month as the balance falls. This instrument assumes a fixed dollar payment held level for the entire payoff — enter your card's current minimum once to see how long an unchanging payment at that level would take.
Does this account for new purchases added to the card?
No — the balance is treated as fixed at the figure entered, with no further charges added during the payoff. A new purchase resets the calculation; re-run it with the higher balance to see the new payoff time, since adding debt while paying it down is exactly what keeps a real card from following this schedule.
References
- Consumer Financial Protection Bureau — Credit cards
- Federal Reserve — Consumer credit (G.19) statistical release
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.