The two APR conventions on one small loan, why a shorter loan shows a higher APR, and what the same £300 costs on a credit card.
A UK payday loan APR compounds the charge over a year: APR = (1 + cost ÷ amount)365 ÷ days − 1. Borrowing £300 for 30 days at 0.8 per cent a day costs £72, so the APR is 1,270 per cent. US lenders state a simple APR instead, fee ÷ amount × 365 ÷ days: a fee of $15 per $100 for 14 days is 391.07 per cent. The same £300 on a 22.9 per cent credit card costs £5.65 for the month.
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 →
Payday lenders like to say the APR is the wrong measure for a loan that lasts a month. It is partly right: the APR is a rate, and what you repay is money. But the APR exists so that a month's borrowing can be compared with a year's, and when the comparison is made, the price is plain. All loan terms below are illustrative.
| Input | Value |
|---|---|
| UK loan amount | £300 |
| UK term | 30 days |
| UK interest, per day | 0.8% |
| US loan amount | $300 |
| US fee | $15 per $100 borrowed |
| US term | 14 days |
| Credit card APR, for comparison | 22.9% |
0.8 per cent a day is the ceiling UK rules set for high-cost short-term credit, and many lenders charge it. Total charges are also capped at 100 per cent of the amount borrowed. US fees vary by state; $15 per $100 is a commonly quoted level.
UK: £300 × 0.008 × 30 days = £72.00; repay £372.00
US: $15 × 300 ÷ 100 = $45.00; repay $345 after 14 days
On the UK loan that is £24 for every £100 for one month: a periodic rate of 24 per cent.
UK consumer credit rules define the APR as an annual equivalent rate: the periodic cost compounded over the number of such periods in a year.
APR = (1 + cost ÷ amount)365 ÷ days − 1
Periods in a year: 365 ÷ 30 = 12.1667
= 1.2412.1667 − 1 = 1,270%
Excel: =(1+72/300)^(365/30)-1
US disclosure rules use a simple annual rate: the finance charge as a share of the amount, scaled to a year without compounding.
APR = fee ÷ amount × 365 ÷ days
= 45 ÷ 300 × 365 ÷ 14 = 15% × 26.0714 = 391.07%
Compounded the UK way, the same loan would show 3,724 per cent.
The two methods give very different numbers for similar loans, so compare APRs only within one country's convention. On the UK loan the simple method gives 292 per cent, which is just 0.8 per cent × 365. The compounded figure is higher because it assumes each month's charge is itself borrowed and charged the next month, which is what happens to a borrower whose unpaid charges are added to the debt and charged again.
| Source | Cost | APR |
|---|---|---|
| Payday loan at 0.8% a day | £72.00 | 1,270% |
| Credit card at 22.9%, interest on the daily balance | £5.65 | 22.9% |
The payday loan costs 12.8 times as much in money for the same month. The card figure is £300 × 22.9% × 30 ÷ 365, the daily method explained in how credit card interest is calculated.
At a fixed 0.8 per cent a day, a longer loan costs more money but shows a lower APR, because there is less compounding left in the year.
| Days | Cost | Simple APR | UK APR |
|---|---|---|---|
| 7 | £16.80 | 292% | 1,614% |
| 14 | £33.60 | 292% | 1,492% |
| 30 | £72.00 | 292% | 1,270% |
| 60 | £144.00 | 292% | 986% |
| 90 | £216.00 | 292% | 802% |
This is why the APR alone can mislead in both directions. A three-month loan with a lower APR costs three times as much money as a one-month loan. At this rate the 100 per cent cap is reached after 125 days.
Where rollovers are allowed, each one pays a new fee and repays nothing. The US $300 loan rolled over four times pays five fees of $45: $225.00 over 70 days, 75 per cent of the amount borrowed, and the borrower still owes the $300. The fees are paid in cash rather than added to the debt, so this is the simple rate repeated, not compounding, but the money is real: three-quarters of the loan gone in ten weeks.
Most payday borrowing answers an emergency, not a want. A small emergency fund, even a few hundred pounds, is what removes the need; see how much an emergency fund should be. If you are already struggling with repayments, free, regulated debt advice is the place to start, and some offers aimed at people in debt are predatory.
A payday loan APR is the periodic charge annualised: 1,270 per cent compounded for £72 on £300 over 30 days in the UK, 391.07 per cent simple for $15 per $100 over 14 days in the US. Read the APR, then read the pounds: £72 against £5.65 on a card. The book's chapter on getting out of debt, and the workbook that prices each debt month by month, are on the free companion page for this book.
Because the APR annualises a charge made for a few weeks. £72 on £300 for 30 days is 24 per cent for the month. Repeated 12.1667 times a year and compounded, that is an APR of 1,270 per cent. The fee is not small: a 22.9 per cent credit card takes about a year to charge what this loan charges in a month.
It is a fair rate but a poor guide to the money. A 7-day loan at 0.8 per cent a day costs £16.80 on £300 and shows an APR of 1,614 per cent; a 90-day loan costs £216.00 and shows 802 per cent. Compare the pounds you will repay as well as the APR, and the loan that looks cheaper by APR may cost more.
Each rollover pays a new fee and leaves the debt unchanged. At $15 per $100 a $300 loan costs $45 every 14 days; rolled over four times, the borrower pays $225.00 in fees over 70 days, 75 per cent of the amount borrowed, and still owes the $300.
This article is one calculation from Personal Finance for Beginners. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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