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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I'm far from convinced by Cameron's plans for Syria

The Prime Minister has a plan for when the bombs drop. But what about after?

In the House of Commons today, the Prime Minister set out a powerful case for Britain to join air strikes against Isil in Syria.  Isil, he argued, poses a direct threat to Britain and its people, and Britain should not be in the business of “outsourcing our security to our allies”. And while he conceded that further airstrikes alone would not be sufficient to beat Isil, he made the case for an “Isil first” strategy – attacking Isil now, while continuing to do what we can diplomatically to help secure a lasting settlement for Syria in which Assad (eventually) plays no part.

I agreed with much of David Cameron’s analysis. And no-one should doubt either the murderous barbarism of Isil in the region, or the barbarism they foment and inspire in others across the world.  But at the end of his lengthy Q&A session with MPs, I remained unconvinced that UK involvement in airstrikes in Syria was the right option. Because the case for action has to be a case for action that has a chance of succeeding.  And David Cameron’s case contained neither a plan for winning the war, nor a plan for winning the peace.

The Prime Minister, along with military experts and analysts across the world, concedes that air strikes alone will not defeat Isil, and that (as in Iraq) ground forces are essential if we want to rid Syria of Isil. But what is the plan to assemble these ground forces so necessary for a successful mission?  David Cameron’s answer today was more a hope than a plan. He referred to “70,000 Syrian opposition fighters - principally the Free Syrian Army (FSA) – with whom we can co-ordinate attacks on Isil”.

But it is an illusion to think that these fighters can provide the ground forces needed to complement aerial bombardment of Isil.  Many commentators have begun to doubt whether the FSA continues to exist as a coherent operational entity over the past few months. Coralling the myriad rebel groups into a disciplined force capable of fighting and occupying Isil territory is a heroic ambition, not a plan. And previous efforts to mobilize the rebels against Isil have been utter failures. Last month the Americans abandoned a $500m programme to train and turn 5,400 rebel fighters into a disciplined force to fight Isil. They succeeded in training just 60 fighters. And there have been incidents of American-trained fighters giving some of their US-provided equipment to the Nusra Front, an affiliate of Al Qaeda.

Why has it proven so hard to co-opt rebel forces in the fight against Isil? Because most of the various rebel groups are fighting a war against Assad, not against Isil.  Syria’s civil war is gruesome and complex, but it is fundamentally a Civil War between Assad’s forces and a variety of opponents of Assad’s regime. It would be a mistake for Britain to base a case for military action against Isil on the hope that thousands of disparate rebel forces can be persuaded to change their enemy – especially when the evidence so far is that they won’t.

This is a plan for military action that, at present, looks highly unlikely to succeed.  But what of the plan for peace? David Cameron today argued for the separation of the immediate task at hand - to strike against Isil in Syria – from the longer-term ambition of achieving a settlement in Syria and removing Assad.  But for Isil to be beaten, the two cannot be separated. Because it is only by making progress in developing a credible and internationally-backed plan for a post-Assad Syria that we will persuade Syrian Sunnis that fighting Isil will not end up helping Assad win the Civil War.  If we want not only to rely on rebel Sunnis to provide ground troops against Isil, but also provide stable governance in Isil-occupied areas when the bombing stops, progress on a settlement to Syria’s Civil War is more not less urgent.  Without it, the reluctance of Syrian Sunnis to think that our fight is their fight will undermine the chances of military efforts to beat Isil and bring basic order to the regions they control. 

This points us towards doubling down on the progress that has already been made in Vienna: working with the USA, France, Syria’s neighbours and the Gulf states, as well as Russia and Iran. We need not just a combined approach to ending the conflict, but the prospect of a post-war Syria that offers a place for those whose cooperation we seek to defeat Isil. No doubt this will strike some as insufficient in the face of the horrors perpetrated by Isil. But I fear that if we want not just to take action against Isil but to defeat them and prevent their return, it offers a better chance of succeeding than David Cameron’s proposal today. 

Stewart Wood is a former Shadow Cabinet minister and adviser to Ed Miliband. He tweets as @StewartWood.