How paying off debt works

Paying off a debt is compound interest experienced from the wrong end. The same arithmetic that grows a saver's balance grows a borrower's too — except this balance is one you owe, and every month it sits there it charges rent. The mechanics below are simple, and every number in them is hypothetical.

Interest accrues on what you still owe

Interest is charged on the outstanding balance — what remains, not what was borrowed. Purely hypothetical arithmetic: a balance of 10,000 at 1% a month accrues 100 of interest in the first month. Left unpaid, that 100 joins the balance and accrues its own interest the next month. This is compound interest with the direction reversed: pointed at the borrower rather than working for the saver.

The anatomy of a payment

A payment is applied in a fixed order: interest first, then whatever remains reduces the balance. Pay 150 against that hypothetical 10,000 and the first 100 covers the month's interest; only 50 reaches the debt itself, leaving 9,950. Pay a minimum of 110 and just 10 gets through — 9,990 remains, and next month's interest is 99.90 instead of 100. A minimum set barely above the interest leaves the base nearly untouched, and a base nearly untouched keeps generating interest. The account can outlast the reasons you opened it.

Extra payments shrink the base

Once the month's interest is covered, every additional unit of payment goes entirely to the balance. Pay 300 instead of 150 and the balance falls to 9,800 rather than 9,950. Next month's interest is then 98 rather than 99.50 — a small difference that repeats every remaining month, and each month's saving lets slightly more of the next payment reach the balance. Shrinking the base shrinks every future interest charge. Compounding runs just as well in reverse; it simply needs feeding.

Two orderings people describe

With several debts, two orderings are commonly described, and both are just arithmetic. Highest-rate-first sends any spare payment to the most expensive balance. This minimises total interest paid — not opinion, arithmetic: at 2% a month, each 100 of balance cleared cancels 2 of monthly interest; at 1% a month, it cancels 1. Smallest-balance-first sends spare payments to the smallest debt instead. It closes accounts sooner, so fewer balances remain open along the way; the interest arithmetic is otherwise unchanged, and where the smallest debt is not also the dearest, it costs more in total interest. Both are common conventions. This article endorses neither — it only reports what the sums do.

What this is not

None of this says whether any particular debt is worth clearing early, or how fast. Some loans charge fees for early repayment, and rates and terms vary in ways no article knows. A payment sent to a balance is also money no longer available for anything else — including the cash buffer described in what an emergency fund is. The arithmetic above holds everywhere. The decision about what to do with it does not, and that part stays yours.