Would Newcastle have to pay back £4bn if its Wonga sponsorship was a loan?

Interest is tricky.

When Wonga announced their intention to sponsor Newcastle United FC, it generated no small amount of opprobrium. Despite the company's best attempts to generate a positive image for itself, it is still largely seen as a payday loan company, preying on the poor for a quick buck. So it was no surprise that smart a demonstration of that fact very quickly made the rounds:

Anything with over 2,000 retweets is going to get fact-checked a lot, and debates soon broke out over whether the number was accurate. Is it?

Wonga's "representative APR" is 4214 per cent. When you take out a loan with it, it decides at the beginning of the period what your interest is, and charges it to you on the total amount of capital borrowed over that period. In other words, it doesn't compound the interest - which makes sense, because it would be hard to compound anything over a loan as short month. As a result, if you were charged an annual interest rate of 4214 per cent, then at the end of a four year period you would have to pay back: 

£24,000,000 + £24,000,000 x 42.14 x 4 = £4,069,440,000.00                                 

(That's the capital, plus four years interest.) A shade over £4bn. So James Dixon is correct.

Except that the 4214 per cent APR is already compounded. As Wonga explains, industry regulations require it to present interest at an annual rate even if it doesn't make annual loans. To do this, it is required to take the amount of interest you would pay on its longest loan, a month-long one, and act as though you rolled it over, taking out larger and larger loans to pay off the interest as you go along. If we compounded Newcastle's loan similarly, then after four years it would owe:

£24,000,000 x (1+42.14)^4 = £83,125,028,034,051.84                                 

That is £83 quadrillion. It's over one hundred times world GDP, and in the ballpark for the total value of everything on earth.

But Wonga would maintain that using that interest rate is unfair. Although they are required to present their representative APR in that manner, they have never, and would never, charge it to a customer. The annual rate of interest which they actually charge is "just" 360 per cent, and the rest is made up of the compounding which they are forced to assume. If Newcastle's loan was taken out at that rate, it would have to pay back:

£24,000,000 + £24,000,000 × 3.6 x 4 = £369,600,000.00                                 

£370m is still quite a lot to pay for £24m, but it's nowhere near billions. And in actual fact, Newcastle wouldn't even pay that much. It's not a person, it's a business, and Wonga have - controversially - launched a division exclusively for lending to businesses. The largest and longest loan it offers is £15,000 for a year, which costs £19,350 to pay back, implying an APR of 29 per cent. If Newcastle borrowed £24m for four years at that rate, then if the interest compounded, it would equal:

£24,000,000 × (1+0.29)^4 = £66,461,491.44                                 

And if it was charged in one lump sum, it would equal:

£24,000,000 + £24,000,000 × 0.29 x 4 = £51,840,000.00                                 

The root of the problem is that Wonga isn't actually in the business of making multi-year, multi-million-pound loans. The assumptions we make in trying to squeeze their business model into a shape that lets us make that comparison are important, because they're the difference between paying back £52m and £83qdrn.

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Alex Hern is a technology reporter for the Guardian. He was formerly staff writer at the New Statesman. You should follow Alex on Twitter.

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No, David Cameron’s speech was not “left wing”

Come on, guys.

There is a strange journalistic phenomenon that occurs when a party leader makes a speech. It is a blend of groupthink, relief, utter certainty, and online backslapping. It happened particularly quickly after David Cameron’s speech to Tory party conference today. A few pundits decided that – because he mentioned, like, diversity and social mobility – this was a centre-left speech. A leftwing speech, even. Or at least a clear grab for the liberal centre ground. And so that’s what everyone now believes. The analysis is decided. The commentary is written. Thank God for that.

Really? It’s quite easy, even as one of those nasty, wicked Tories, to mention that you actually don’t much like racism, and point out that you’d quite like poor children to get jobs, without moving onto Labour's "territory". Which normal person is in favour of discriminating against someone on the basis of race, or blocking opportunity on the basis of class? Of course he’s against that. He’s a politician operating in a liberal democracy. And this isn’t Ukip conference.

Looking at the whole package, it was actually quite a rightwing speech. It was a paean to defence – championing drones, protecting Britain from the evils of the world, and getting all excited about “launching the biggest aircraft carriers in our history”.

It was a festival of flagwaving guff about the British “character”, a celebration of shoehorning our history chronologically onto the curriculum, looking towards a “Greater Britain”, asking for more “national pride”. There was even a Bake Off pun.

He also deployed the illiberal device of inculcating a divide-and-rule fear of the “shadow of extremism – hanging over every single one of us”, informing us that children in UK madrassas are having their “heads filled with poison and their hearts filled with hate”, and saying Britain shouldn’t be “overwhelmed” with refugees, before quickly changing the subject to ousting Assad. How unashamedly centrist, of you, Mr Prime Minister.

Benefit cuts and a reduction of tax credits will mean the Prime Minister’s enthusiasm for “equality of opportunity, as opposed to equality of outcome” will be just that – with the outcome pretty bleak for those who end up losing any opportunity that comes with state support. And his excitement about diversity in his cabinet rings a little hollow the day following a tubthumping anti-immigration speech from his Home Secretary.

If this year's Tory conference wins the party votes, it’ll be because of its conservative commitment – not lefty love bombing.

Anoosh Chakelian is deputy web editor at the New Statesman.