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.

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Emily Thornberry heckled by Labour MPs as tensions over Trident erupt

Shadow defence secretary's performance at PLP meeting described as "risible" and "cringeworthy". 

"There's no point trying to shout me down" shadow defence secretary Emily Thornberry declared midway through tonight's Parliamentary Labour Party meeting. Even by recent standards, the 70-minute gathering was remarkably fractious (with PLP chair John Cryer at one point threatening to halt it). Addressing MPs and peers for the first time since replacing Maria Eagle, Thornberry's performance did nothing to reassure Trident supporters. 

The Islington South MP, who voted against renewal in 2007, said that the defence review would be "wide-ranging" and did not take a position on the nuclear question (though she emphasised it was right to "question" renewal). She vowed to listen to colleagues as well as taking "expert advice" and promised to soon visit the Barrow construction site. But MPs' anger was remorseless. Former shadow defence minister Kevan Jones was one of the first to emerge from Committee Room 14. "Waffly and incoherent, cringeworthy" was his verdict. Another Labour MP told me: "Risible. Appalling. She compared Trident to patrolling the skies with spitfires ... It was embarrassing." A party source said afterwards that Thornberry's "spitfire" remark was merely an observation on changing technology. 

"She was talking originally in that whole section about drones. She'd been talking to some people about drones and it was apparent that it was absolutely possible, with improving technology, that large submarines could easily be tracked, detected and attacked by drones. She said it is a question of keeping your eye on new technology ... We don't have the spitfires of the 21st century but we do have some quite old planes, Tornadoes, but they've been updated with modern technology and modern weaponry." 

Former first sea lord and security minister Alan West complained, however, that she had failed to understand how nuclear submarines worked. "Physics, basic physics!" he cried as he left. Asked how the meeting went, Neil Kinnock, who as leader reversed Labour's unilateralist position in 1989, simply let out a belly laugh. Thornberry herself stoically insisted that it went "alright". But a shadow minister told me: "Emily just evidently hadn't put in the work required to be able to credibly address the PLP - totally humiliated. Not by the noise of the hecklers but by the silence of any defenders, no one speaking up for her." 

Labour has long awaited the Europe split currently unfolding among the Tories. But its divide on Trident is far worse. The majority of its MPs are opposed to unilateral disarmament and just seven of the shadow cabinet's 31 members share Jeremy Corbyn's position. While Labour MPs will be given a free vote when the Commons votes on Trident renewal later this year (a fait accompli), the real battle is to determine the party's manifesto stance. 

Thornberry will tomorrow address the shadow cabinet and, for the first time this year, Corbyn will attend the next PLP meeting on 22 February. Both will have to contend with a divide which appears unbridgeable. 

George Eaton is political editor of the New Statesman.