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.

Front page of Wonga.com

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

Jeremy Corbyn delivers a speech on the arts in north London on September 1, 2015. Photograph: Getty Images.
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Can Labour MPs force Corbyn to bring back shadow cabinet elections?

It is not up to the parliamentary party whether the contests are reintroduced. 

Soon after Jeremy Corbyn became the frontrunner in the Labour leadership contest, it was reported that he intended to bring back shadow cabinet elections. But as I later wrote, that's not the case. Corbyn has resolved that he will maintain the right to appoint his own team, rather than having it elected by MPs (as was the case before Ed Miliband changed the system in 2011). As he wrote in the NS: "Whoever emerges as leader on 12 September needs a shadow cabinet in place as soon as possible. I will appoint a strong, diverse shadow cabinet to hold this government to account from day one."

Now, ahead of his likely victory a week on Saturday, Corbyn is under pressure from some MPs to reverse his stance. Barry Sheerman, the former education select commitee chair, told me that he wanted a "serious discussion" within the PLP about the return of the elections. While some support their reinstatement on principled grounds, others recognise that there is a tactical advantage in Corbyn's opponents winning a mandate from MPs. His hand would be further weakened (he has the declared support of just 14 of his Commons colleagues). 

But their reinstatement is not as simple as some suggest. One senior MP told me that those demanding their return "had not read the rule book". Miliband's decision to scrap the elections was subsequently approved at party conference meaning that only this body can revive them. A simple majority of MPs is not enough. 

With Corbyn planning to have a new team in place as soon as possible after his election, there is little prospect of him proposing such upheaval at this point. Meanwhile, Chuka Umunna has attracted much attention by refusing to rule out joining the left-winger's shadow cabinet if he changes his stances on nuclear disarmament, Nato, the EU and taxation (a lengthy list). Umunna is unlikely to remain on the frontbench but having previously pledged not to serve, he now recognises that there is value in being seen to at least engage with Corbyn. Were he to simply adopt a stance of aggression, he would risk being blamed if the backbencher failed. It is one example of how the party's modernisers recognise they need to play a smarter game. I explore this subject further in my column in tomorrow's NS

George Eaton is political editor of the New Statesman.