The True Cost of Minimum Payments: A Mathematical Autopsy

There is a number on your credit card statement that is not labelled as what it is. It is labelled "Minimum Payment." It should be labelled "The Minimum We Need You to Pay to Maximise Our Interest Revenue." The gap between those two descriptions is worth, depending on your balance, somewhere between £3,000 and £20,000 over your lifetime.

The Formula

Credit card interest in the UK is calculated using a daily periodic rate (DPR):

DPR = APR ÷ 365

For a card at 22.9% APR: DPR = 22.9 ÷ 365 = 0.06274%/day

Interest for a given month = Average Daily Balance × DPR × Days in Month

On a £3,000 balance at 22.9% APR: Monthly interest = £3,000 × 0.06274% × 30 = £56.47

This is the baseline. Everything else flows from this calculation.

Why the Minimum Payment Is Designed to Minimise Progress

Most UK credit card minimum payments are calculated as:

Greater of:

• 1–2.5% of the outstanding balance, OR
• £25

Plus, in many cases, any interest and fees from that month.

For a £3,000 balance at 22.9% APR with a 1% minimum:

• Monthly interest: £56.47
• 1% of balance: £30
• Minimum payment: £56.47 + £30 = £86.47
• Principal reduction: £30 (the 1% portion)
• Interest consumed: £56.47 (65.3% of payment)

After one month, the balance is £2,970. The percentages barely change. This is the trap: the payment is nominally "covering" the debt, but 65.3% of it is immediately recycled back to the lender as profit.

The Shrinking Minimum: Compounding in Reverse

The cruelest feature of minimum payment mechanics is that the minimum itself decreases as the balance decreases. In month 1, the minimum on a £3,000 balance at 22.9% (1% minimum) is £86.47. In month 12, with the balance reduced to approximately £2,784, the minimum falls to ~£80.47.

This creates a compounding-in-reverse effect. As the balance falls:

1. Monthly interest falls (slightly)
2. Required minimum falls
3. Principal reduction per payment falls
4. Progress slows

This is not linear decay, it is exponential slowdown. The first £500 of principal reduction takes about 20 months. The last £500 takes about 40 months, even though the balance is much smaller, because the payment has shrunk along with the balance.

The result: a debt that is geometrically designed to take as long as possible to clear.

The Full Amortisation Table: What Minimum Payments Actually Do

Here is what happens to a £3,000 balance at 22.9% APR under minimum payments (1% + interest), calculated precisely:

After 10 years of minimum payments on a £3,000 balance: you still owe £1,397. You have paid £5,200+ and cleared less than half the original debt. The bank has received £3,200+ in pure interest.

This is not a worst-case scenario. This is the mathematically precise outcome of following the minimum payment instruction.

The Comparison: Fixed Payments

The antidote to the shrinking minimum is the fixed payment. Set a standing order for a specific amount, regardless of what the statement says, and keep it there as the balance falls.

On the same £3,000 at 22.9% APR:

The fixed payment of £120, just £33.53 more than month 1's minimum, saves £1,582 and clears the debt 18.5 years faster. The extra £33.53/month is worth £1,582. That is a 33:1 return on the incremental payment.

The Power of the First Extra Pound

This is the most counter-intuitive insight in debt mathematics: the first extra pound of monthly payment has a disproportionately large impact compared to subsequent extra pounds.

On a £3,000 balance at 22.9% APR:

• Paying £1 extra per month (£87 instead of £86): saves £110 in interest, 6 months faster
• Paying £2 extra (£88): saves £215 in interest, 1 year faster
• Paying £10 extra (£96): saves £920 in interest, 5.5 years faster
• Paying £20 extra (£106): saves £1,500 in interest, 8 years faster

The reason for this disproportionate impact: the sooner you reduce the balance, the sooner you stop accruing interest on that portion of the debt. Each extra pound paid today prevents not just its own interest but also the interest that would have accumulated on it for years.

Daily Interest: The True Cost of Waiting

On a £3,000 balance at 22.9% APR, you are being charged:

• £1.88 per day in interest
• £56.47 per month
• £677 per year

Every single day you delay making an extra payment costs £1.88. Every day you wait for the right moment to start attacking the debt, you are paying the lender £1.88 in interest.

This reframe, from "£3,000 total debt" to "£1.88/day draining from your account", is why the Interest Burner exists. The daily number is viscerally comprehensible in a way that total balances are not. It turns an abstract financial consideration into an immediate, daily cost that can be compared to the daily price of a coffee, a lunch, or a subscription.

Practical Application

Step 1: Use the Interest Burner to find your exact daily bleed on each debt. Step 2: Identify the highest-APR debt, this is where the minimum payment trap is most expensive. Step 3: Set a fixed standing order for this debt, above the minimum. Even £20/month above the minimum makes a significant difference. Step 4: Use the Overpayment Squeezer to model exactly how different fixed payment levels affect your debt-free date. Step 5: Track every payment in DaysBack. Watch the days saved climb.

For free UK debt advice: MoneyHelper (0800 138 7777) and StepChange (0800 138 1111).