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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Voters are turning against Brexit but the Lib Dems aren't benefiting

Labour's pro-Brexit stance is not preventing it from winning the support of Remainers. Will that change?

More than a year after the UK voted for Brexit, there has been little sign of buyer's remorse. The public, including around a third of Remainers, are largely of the view that the government should "get on with it".

But as real wages are squeezed (owing to the Brexit-linked inflationary spike) there are tentative signs that the mood is changing. In the event of a second referendum, an Opinium/Observer poll found, 47 per cent would vote Remain, compared to 44 per cent for Leave. Support for a repeat vote is also increasing. Forty one per cent of the public now favour a second referendum (with 48 per cent opposed), compared to 33 per cent last December. 

The Liberal Democrats have made halting Brexit their raison d'être. But as public opinion turns, there is no sign they are benefiting. Since the election, Vince Cable's party has yet to exceed single figures in the polls, scoring a lowly 6 per cent in the Opinium survey (down from 7.4 per cent at the election). 

What accounts for this disparity? After their near-extinction in 2015, the Lib Dems remain either toxic or irrelevant to many voters. Labour, by contrast, despite its pro-Brexit stance, has hoovered up Remainers (55 per cent back Jeremy Corbyn's party). 

In some cases, this reflects voters' other priorities. Remainers are prepared to support Labour on account of the party's stances on austerity, housing and education. Corbyn, meanwhile, is a eurosceptic whose internationalism and pro-migration reputation endear him to EU supporters. Other Remainers rewarded Labour MPs who voted against Article 50, rebelling against the leadership's stance. 

But the trend also partly reflects ignorance. By saying little on the subject of Brexit, Corbyn and Labour allowed Remainers to assume the best. Though there is little evidence that voters will abandon Corbyn over his EU stance, the potential exists.

For this reason, the proposal of a new party will continue to recur. By challenging Labour over Brexit, without the toxicity of Lib Dems, it would sharpen the choice before voters. Though it would not win an election, a new party could force Corbyn to soften his stance on Brexit or to offer a second referendum (mirroring Ukip's effect on the Conservatives).

The greatest problem for the project is that it lacks support where it counts: among MPs. For reasons of tribalism and strategy, there is no emergent "Gang of Four" ready to helm a new party. In the absence of a new convulsion, the UK may turn against Brexit without the anti-Brexiteers benefiting. 

George Eaton is political editor of the New Statesman.