Enter a balance, a rate and the monthly payment you have in mind. The calculator returns the number of months, the total interest, and — the part most calculators skip — whether that payment clears the debt at all. Below a certain figure it does not, and no amount of patience will change that.
Someone has decided on a monthly amount they can afford and wants to know when the debt will be gone, and whether that amount is actually enough to make progress.
Before any schedule or formula, there is a single figure worth knowing: the first month's interest. On a $5,000 balance at 22%, that is $91.67. Any payment above $91.67 reduces the debt. Any payment at or below it does not reduce the debt at all — the balance stays the same or grows, and it will still be there in ten years.
This is not a matter of degree. At $92 the balance falls, slowly. At $91 it rises. The line is that sharp, and it sits at a number most people have never calculated. The calculator reports it directly so the question can be answered before choosing a payment rather than after years of paying one.
Once the payment clears the interest, the arithmetic is well behaved and the closed form above gives the answer exactly. The months required fall steeply as the payment rises, which is why raising a payment by a modest amount shortens the term by far more than a modest amount.
$5,000 at 22% clears in 34 months at $200 a month, and in 26 months at $250. That is a 25% increase in the payment for a 24% reduction in the term — roughly proportional. But the interest saving is not proportional at all: it falls from $1,800 to $1,500.
The effect grows with the balance. On $20,000 at 22%, paying $500 a month takes 71 months; paying $600 takes 53. The extra $100 a month removes a year and a half, and it does so because every extra dollar reduces the balance that the next month's interest is charged on — and that saving compounds for the whole remaining term.
This is the same compounding that works against a borrower on the way up, running in the other direction. It is also why paying extra early is worth far more than paying extra late: an extra dollar in month one saves interest for every month that follows it.
The formula assumes the rate never changes, the payment never changes, and no new charges are added. Revolving credit fails all three. A missed payment typically triggers a penalty APR, which can push the payment below the monthly interest and turn a plan that was working into one that is not.
It also assumes the payment is made at the end of each month. Paying earlier in the cycle reduces the average balance the interest is calculated on, which saves a little more. The effect is real but small compared with the size of the payment itself.
And it says nothing about whether the payment is affordable. A plan that clears a debt in 34 months is worthless if the 34th month is the one where something else goes wrong. The payment has to survive a bad month, not just an average one.
n = −ln(1 − i·B ÷ PMT) ÷ ln(1 + i) where i = APR ÷ 12
The logarithm is only defined when PMT is greater than i·B — that is, when the payment covers the interest. Below that line the expression has no real answer, because the balance genuinely never falls. This calculator reports that case instead of returning a meaningless number.
The first month's interest is $91.67, so a $200 payment reduces the balance by $108.33. The debt clears after 34 months, with $1,800 of interest paid and $6,800 handed over in total. This is the ordinary case: the payment comfortably clears the interest and the schedule behaves as expected.
Dropping the payment to $100 — which is still above the $91.67 of monthly interest — stretches the payoff from 34 months to 137. The interest rises from $1,800 to $8,700, and the total paid from $6,800 to $13,700. The payment fell by half and the cost nearly quintupled, because so much of each payment now goes to interest rather than principal.
At $80 a month, the payment is below the $91.67 of monthly interest. The balance grows every month and there is no payoff date — not in 137 months, not in 1,370. The calculator reports that the debt never clears, and it also reports the $91.67 that would have to be exceeded to make any progress at all. That figure is the most useful number on the page for anyone in this position.
Find the first month's interest — the balance multiplied by the annual rate divided by twelve. If your payment is above that, the number of months is −ln(1 − iB/PMT) ÷ ln(1 + i), where i is the monthly rate. If the payment is at or below it, the debt never clears and no formula will give you a date.
Because the extra money reduces the balance that every future month's interest is calculated on. On $5,000 at 22%, paying $200 instead of $100 turns 137 months into 34 and cuts the interest from $8,700 to $1,800. The saving compounds for the whole remaining term, which is why it is larger than the extra payments themselves.
The balance grows. There is no payoff date, at any horizon, because each month adds more interest than the payment removes. This is common on high-rate balances paid at a small fixed amount, and it is worth checking before committing to a payment plan rather than after.
The highest rate first costs the least in total, because it removes the most expensive interest earliest. The smallest balance first clears an account sooner, which some people find easier to sustain. Both work; the difference in cost is real but smaller than the difference between paying extra and not.