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What a minimum payment actually does to a credit card balance

£81.53 leaves the account and £20.46 reaches the debt. On minimums alone the card takes 258 months, and 1.78 times what was borrowed goes out of the door.

Julian R. Sterling · from Personal Finance for Beginners

A minimum payment is not a small repayment. On an ordinary card at an ordinary rate, 74.9% of it is interest and the rest — £20.46 out of £81.53 — is the only part that touches what is owed.

Worked in full in Personal Finance for Beginners by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →

That is the trap, and it is one number. Everything else follows from it.

The first payment, in full

A minimum of 2.5 per cent of the statement balance, with a floor. Ordinary terms, ordinary card.

The first payment	Amount
Balance on the card	£3,200
Interest rate	22.9%
Interest charged this month	£61.07
Minimum payment due	£81.53
of which is interest	£61.07
of which reaches the balance	£20.46
Share of the payment that is interest	74.9%

£81.53 leaves the account. £20.46 reaches the debt. The bank is not doing anything improper: the minimum is calculated as a percentage of the balance, and at 22.9% a year the interest alone eats three quarters of it.

The mechanism is self-perpetuating. Because the minimum is a percentage of the balance, it falls as the balance falls — so the part that reduces the debt shrinks in step with the debt. The card is designed to be repaid slowly, and it is.

Five debts, and what minimums do to them

Plus £250 a month of surplus, beyond every minimum. That surplus is the whole of the plan.

Debt	Balance	Rate	Monthly minimum
Store card	£680	29.9%	£20.00
Credit card A	£3,200	22.9%	£81.53
Credit card B	£1,450	18.9%	£36.82
Personal loan	£2,100	12.5%	£95.00
Car loan	£6,500	7.9%	£180.00
Total owed	£13,930

Pay the minimums and nothing else, and the set clears in 258 months — 21.5 years. Total interest £10,886, on £13,930 borrowed. In total, 1.78 times what was borrowed leaves the account.

What £250 a month does

Now add a surplus — £250 a month beyond every minimum — and send it all at one debt at a time. Two orderings are usually argued about: highest interest rate first, or smallest balance first.

Same debts, same rates. The only difference is where the surplus goes.

Plan	Months	Years	Total interest	Total repaid
Minimums only, no surplus	258	21.5	£10,886	£24,816
Avalanche — highest rate first	30	2.5	£2,033	£15,963
Snowball — smallest balance first	31	2.6	£2,257	£16,187

£250 a month turns 21.5 years into 2.5, and £10,886 of interest into £2,033. The surplus is worth £8,853 and 228 months. Whether it is aimed at the highest rate or the smallest balance changes the answer by £224.

The argument people have, priced

Highest-rate-first is arithmetically optimal; smallest-balance-first is argued for on motivation. Here is what the motivation costs on this set of debts: £224 in total, or £7.46 a month over the life of the plan, plus one extra month.

That is a real number and a small one. Anyone who will actually stick to the smallest-balance order, and would not stick to the other, is buying persistence for £7.46 a month. Both plans beat minimums by more than fifteen times that. The method matters far less than the surplus existing at all.

The step that is worth more than the argument

Both plans above send only the £250 surplus at the target debt. But when a debt clears, its minimum stops being owed — and that money is already leaving the account every month. Roll it into the next debt and nothing changes in the household budget.

Rolling a cleared debt’s minimum into the next one costs nothing: the money was already leaving the account.

Plan	Months	Total interest
Avalanche, surplus only	30	£2,033
Avalanche, freed minimums rolled in	26	£1,932
Snowball, surplus only	31	£2,257
Snowball, freed minimums rolled in	26	£2,012

Rolling the freed minimums saves £245 on the snowball and £101 on the avalanche, and takes 5 and 4 months off respectively. On the snowball that is more than the entire cost of choosing the snowball in the first place — £245 against £224. The step nobody argues about is worth more than the step everybody argues about.

What to do with this

Work out one number before anything else: on your largest card, what does this month's minimum actually reduce the balance by? Interest is the balance times the rate divided by twelve; the rest of the minimum is the answer. If that number is small relative to the payment, the plan is not the minimum — the plan is the surplus.

Then check whether the two orderings even differ. If the highest-rate debt happens also to be the smallest, the argument is moot — and it is worth ten seconds of checking before agonising.

And when a debt clears, move its payment onto the next one the same month. It is the cheapest acceleration available, because the money has already left the budget.

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