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On adverts for payday loan deals (UK), the representative APR is always displayed in small print, by law.

I always feel as though these loans, with their x-thousand % interest rates are ripping off those most in need.

However, I have stumbled across this claim on Wonga.com;

We don't actually charge thousands of percent in interest

In fact we don't charge anything like the large Representative APR

Wonga charges the equivalent of just under 1% interest per day and that rate is applied to the loan amount and transmission fee for the period of the short term loan - usually between one and 31 days. The annual rate of interest is 360%. We know this may be hard to believe, because of the much larger Representative APR we are obliged to display. But that's because the calculation required by law means that, where a loan is not taken out for a year, the interest rate must be compounded the same number of times the actual loan period would fit into a year. Because an annualised measure is distorting over short periods of time, we always show the total cost of repayment very clearly too.

The current Wonga representative APR is 4214%, so how can they claim it is in fact 360% ?

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AnthonyBlake
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    OMG, seriously? And I though credit card charging 1.2% a month was a total rip-off. – vartec Feb 14 '12 at 17:11
  • @vartec oh yes, they seem all the rage at the moment in the UK, and target the most desperate. – AnthonyBlake Feb 14 '12 at 20:04
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    it's still shockingly high, eg. Provident in Poland, which as I just checked offers EAR of 59%-137%, caused outrage, which has lead to Anti-Usury Act to be passed. This legally limits APR to no more than 4 times the lombard rate (curr. @ 6%) and no more than 5% of surcharges. However, companies circumvent that by creating charges which are not covered by this law. Anyway, I'm shocked to see that Provident UK (http://www.providentpersonalcredit.com/) offers EAR of 272%-1068%. Wow. – vartec Feb 14 '12 at 20:44
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    funny fact, £100 at Wonga’s APR for 7 years is £23.5 trillion or ($36.9 trillion), twice as much as US national debt. http://blog.moneysavingexpert.com/2011/09/21/fact-borrowing-100-at-wongas-apr-costs-more-than-the-us-national-debt-over-14-trillion-after-7-years/ – vartec Feb 14 '12 at 20:58
  • Quite obviously Wonga is lying. They are indeed charging over 4000% APR. And if you borrow £100, and a month later your mother borrows £130 so you can pay back the loan, and a month later your uncle borrows £170 so your mum can pay back the loan then you can see where this goes. – gnasher729 Nov 06 '15 at 23:49
  • closed? I'd say its a notable claim and challenging Psuedo-mathematics – AnthonyBlake Nov 09 '15 at 09:44

1 Answers1

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Let's see if I can get my high school maths right.

With simple interest, the formula is simple.

If you borrow $100, at 6% per annum simple interest for half of a year, you must pay back:

$100 * (6/100 * 1/2 year) = $3 interest, plus the original $100 principal.

But, if you borrow with compound interest, then you have to pay interest on the unpaid interest. The rate of compounding (how often you calculate the interest) makes a difference.

If it compounds every 6 months, it is still the same amount: $3.

If it compounds ever 3 months - i.e. twice - it is:

$100 * ((1 + (6/100 * 1/2 year)/2)2 - 1) = $3.022 interest, plus the original $100 principal.

If it compounds every day - i.e. 183 times - it is:

$100 * ((1 + (6/100 * 1/2)/183)183 - 1) = $3.045 interest, plus the original $100 principal.

So the frequency of the compounding is important, even though the nominal interest rate (6% per annum) didn't change. The nominal rate is also known as the Nominal Annual Percentage Rate (APR).

Governments (and most legitimate businesses) understand that the nominal APR is misleading, and they insist that people publish the Representative APR (a.k.a. Effective APR, EAR, Annualised APR, or AAPR) which is standardised as being the interest rate you'd pay if you borrowed for one year.

Now, lets use Wonga's figures, to see how the representative figures look:

If you borrow $100 for 1 year at a nominal rate of interest of 360% per annum compounding every day (non-leap year), you actually pay:

$100 * ((1 + (360/100)/365)365 - 1) = $3495.84 interest, plus the original $100.

This corresponds to an Representative APR of 3495%, but there may be other charges that make the real figure even higher.

Now, Wonga is right that, because the loan is much shorter than a year, your total bill will not come to that figure. However, it is a representative figure because it allows you to compare their interest rates to other lenders.

Wonga can honestly quote 360% (or 1% per day) as the Nominal APR, but (as they admit) the regulations require them to also state the Representative APR which is much higher.

It appears that they charge simple interest over the short period of the loan (plus a fee), which I assume means the Representative APR represents the worst case of a 1 day loan. If you borrow for 30 days, the annualised APR would be lower.

Here's one online tool to try this stuff out for yourself. It computes the last figure as $3522.43 - I am hoping the difference is taking into account leap years and rounding errors.

Oddthinking
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  • Aha... it is understandable then that law requires a standard Representative APR calculation so that products can be compared on a par. for example, it appears that using a credit card is typically considerably cheaper than taking a payday loan. – AnthonyBlake Feb 14 '12 at 14:54
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    A credit-card would generally be much cheaper. I don't believe the Representative APR law applies in Australia for credit-cards. Mine advertises itself as 19.99% per annum, and then underneath admits it is 0.054767% per day, which is a representative APR of 22.12%. Not as clear usury as Wonga, but still high and still a shonky way to advertise. – Oddthinking Feb 14 '12 at 15:10
  • @Oddthinking: when comparing with credit cards, you have to also take in account, that "payday loan" is basically included for free in most of them (ie. if you have them set to "total payment", it's charged monthly, after payday w/o any additional costs). Many delay payment even further, for example one of CCs I have, charges on 5th of following month, but if transaction is made on 11th or later it charges month after that, thus you always get between 24 and 54 days of payment delay for free. – vartec Feb 15 '12 at 11:56
  • @vartec: True, as long as the loan is for a purchase (not a cash withdrawal), because then they can charge the vendor a transaction fee to cover their missing interest. – Oddthinking Feb 15 '12 at 12:18