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.
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.
That is the trap, and it is one number. Everything else follows from it.
The first payment, in full
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%
A minimum of 2.5 per cent of the statement balance, with a floor. Ordinary terms, ordinary card.
£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
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
Plus £250 a month of surplus, beyond every minimum. That surplus is the whole of the plan.
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.
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
Same debts, same rates. The only difference is where the surplus goes.
£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.
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 a cleared debt’s minimum into the next one costs nothing: the money was already leaving the account.
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.
The workbook behind this article
Every figure above is a live formula in the companion file for
Personal Finance for Beginners, which also has a sheet for one debt of
your own: your balance, your rate, your payment. It is free, and it needs no account and no
email address.
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