How long until this is paid off?

How many months a balance takes to clear at the payment you are actually making, what the credit costs over that time, and what happens when the payment is smaller than the interest. It is one balance you are not adding to, so an account you keep spending on never gets here, and it counts no fee, insurance or early-settlement charge.

At 1,500 a month a balance of 30,000 clears in 24 months, having paid 35,935, of which 5,935 is what the credit cost, assuming the rate holds for the whole run.

The balance is run month by month rather than solved in one line. Each month the interest is a twelfth of the annual rate applied to whatever is still owed, the payment comes off what that leaves, and the count stops the month the balance reaches zero. The last instalment is trimmed to the remainder, which is what a real agreement does — rounding the month up and multiplying the payment by it would overstate the total by most of one instalment, and the total is the figure most readers came for.

There is a payment at which none of this happens. When the payment is at or below one month's interest, the balance is the same size at the end of the month as it was at the start, and it stays that size for as long as the arrangement runs. There is no number of months that answers that, so the calculator prints none and says what the interest alone comes to instead. A very large number of months would be the wrong answer twice over: it would be arithmetic that does not converge, and it would tell somebody making no progress that they were making slow progress.

Between those two there is a third state, and it is separated on purpose. A payment that covers the interest by a little does bring the balance down every month, but can take longer than a century to finish. That is not a payment failing to cover the interest, and saying so would be contradicted by the falling line drawn beside it. The card says the balance falls and does not clear, which is the true sentence.

each month, interest = balance × rate ÷ 12, and the payment comes off what is left

The count stops the month the balance reaches zero, and the last instalment is whatever remains rather than a full payment.

A worked example

A balance of 30,000 at 18% a year, paid at 1,500 a month, clears in 24 months. The first month's interest alone is 450, so 1,050 of that first payment reaches the balance and the rest pays for the credit; by the end 5,935 has gone on interest and 35,935 has been paid in all.

What it assumes

• The rate is fixed for the whole run and applied monthly, at a twelfth of the annual figure. A card that reprices, or one whose introductory rate ends part way through, is a different loan from that date on.
• The payment is made in full and on time every month. A month missed adds its own interest to the balance and moves every month after it, by more than the one payment.
• Nothing is added to the balance. On a card that is much the harder of the two assumptions, because the account stays open and the balance the figure was calculated on is not the balance at the end of the week.
• No fee, insurance premium or early-settlement charge is counted. Each of them changes what the arrangement costs without changing the rate it advertises, which is why the total here is a floor rather than a forecast.