Money

Short Term Loan APR Explained

“Wonga lends at over 5000% APR!” I hear people cry on a daily basis. Well, yes… but honestly, that means very little.

There are a lot of things wrong with short term loan companies, but funnily enough high APRs are not one of them, because for loans shorter than a year they don’t reflect how much you pay.

Take this example we use on the Smart-Pig website.

Say someone offers you a loan of £100 for 1 day. You have to repay £101.

Q: How much has the loan cost?
A: £1
Q: What's that as a %?
A: 1%
Q: So what is the APR of this loan?
A: 3678%

See the issue? How does 3678% relate to the cost of the loan? How is it relevant? Well, it’s the cost of taking out a loan on the same terms again and again and again over the course of a year, borrowing more each time to pay off the last loan. And that’s just not possible. Either way, £1 to borrow £100 for a day sounds pretty reasonable – you’d buy a friend a pint if they gave you an £100 advance. It’s also more sensitive to loan duration than the actual price of the loan, which can be misleading.

So how do we come to 3678%? Well, the APR formula is a bit complex, and allows for multiple drawings and repayments. Luckily many terms of the full calculation drop out when there is only one “drawdown” and one “repayment”.

If:

x = APR in %
c = amount borrowed (£100)
d = total amount to be repaid (in one payment on the due date £101)
s = duration of the loan in years 9so number of days the loan is for divided by 365 days in the year, 1/365)

Then:

x=-100x((c/d)^(1/S)-1)x(c/d)^-(1/S)

APR% = -100 x ((100/101)^(1/365)-1) x ((100/101)^-(1/365)) = 3,678%

And the pint? In my local that’s about £3… 4,848,172% APR.

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× Warning: Late repayment can cause you serious money problems. For help, go to moneyadviceservice.org.uk