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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A tale of two electorates: will rural France vote for Emmanuel Macron?

His chief rival, Marine Le Pen, was campaigning as the “candidate of the forgotten” years before Donald Trump entered politics.

It was a wet night in Paris, but hundreds of people were queuing outside the Antoine Theatre. It was standing room only to see Emmanuel Macron tonight, as it has been for weeks.

The 39-year-old former investment banker gave his usual energetic performance, delivering a well-practised pitch for a progressive, business-friendly and unabashedly pro-European France. His reward: a standing ovation and chants of Macron, président!

This theatre appearance on 8 March was an appropriate stop for a campaign that has been packed with more political drama than a series of House of Cards. Ahead of the first round of voting in the French presidential election on 23 April, the centrist independent has gone from underdog to the man most likely to beat the Front National’s Marine Le Pen. His other main rival, François Fillon of the right-wing Republicans, has been hampered by allegations that he paid his wife and children as parliamentary assistants, despite scant evidence of them doing any work.

Macron, meanwhile, has been attracting support from disenchanted voters on both left and right.

“It’s a new party, a new movement, a new face,” said Claire Ravillo-Albert, a 26-year-old human resources student and ex-Socialist in the queue outside the theatre. “We’re worlds away from the old Socialists and the Republicans here.”

Macron is not a typical outsider, having made millions in banking before serving as an advisor to François Hollande and as economy minister from 2014 to 2016. Nor can his ideas be described as radical. He is “of the left”, he says, but “willing to work with the right”.

For many he seems to embody an enticing alternative to the tired political class. Macron has never run for office before and if successful, would be the youngest president of the modern French republic. Many recruits to his one-year-old party En Marche! are young and relatively new to politics.

“I think he’ll change the French political landscape, and we need that,” said Olivier Assouline, a bank worker in an immaculate grey suit. “He knows business, he knows the state. I think he’s the right person at the right moment,” said the 44-year-old, who previously voted for right-winger Nicolas Sarkozy.

Many queuing for the rally were underwhelmed by Socialist achievements over the past five years – not least the dismal state of the economy – and had little enthusiasm for Fillon, a social conservative and economic Thatcherite.

Macron’s manifesto sticks firmly to the centre-ground. He has promised tax cuts for companies and millions of poor and middle-class families, as well as a few offbeat ideas like a one-off 500-euro grant for each 18-year-old to spend on books and cultural activities.

“With his central positioning, Macron is taking from everywhere – he has the capacity to seduce everyone,” says Frédéric Dabi, deputy director at the polling company IFOP. They estimate that Macron will take half the votes that went to Hollande when he won the last presidential election in 2012, and 17 per cent of those that went to runner-up Sarkozy.

Outside the theatre, the line was split between voters from the left and the right. But there was one word on almost everyone’s lips: Europe. At a time of continental soul-searching, Macron’s converts have chosen a candidate who backs the European Union as a guarantor of peace and celebrates free movement.

“He’s unusual in that he puts that centre-stage,” said Emma, a 27-year-old legal worker who preferred to be identified by her first name only. “Macron offers a good compromise on economic issues. But for me it’s also about Europe, because I think that’s our future.”

With Fillon and Socialist candidate Benoît Hamon both languishing behind in the polls, the second round of the presidential vote, on 7 May, is likely to be a contest between Macron and Le Pen. These are both candidates who claim to have moved beyond left-right politics, and who are both offering opposing visions of France.

This is also a tale of two electorates. Le Pen was campaigning as the “candidate of the forgotten” years before Donald Trump entered politics, traipsing around deindustrialised towns appealing to those who felt left behind by globalisation.

In the queue to see Macron were lawyers, PR consultants, graphic designers; students, gay couples and middle-class Parisians of multiple ethnicities. These are the representatives of a cosmopolitan, successful France. It was hard not to be reminded of the “metropolitan elite” who voted against Brexit.

Macron has called for investment in poorer communities, and his campaign staff pointedly invited onstage a struggling single mother as a warm-up act that night.

Yet his Socialist rival, Benoit Hamon, accuses him of representing only those who are doing pretty well already. It is hard for some to disassociate Macron from his education at the Ecole Nationale d’Administration – university of choice for the political elite – and his career at Rothschild. One infamous incident from early in the campaign sticks in the memory, when he told a pair of workers on strike: “You don’t scare me with your t-shirts. The best way to pay for a suit is to work.” For Macron, work has usually involved wearing a tie.

IFOP figures show him beating Le Pen soundly in when it comes to the voting intentions of executives and managers – 37 per cent to her 18 per cent. But when it comes to manual workers, she takes a hefty 44 per cent to his 17. He would take Paris; she fares better in rural areas and among the unemployed.

If Frédéric Dabi is to be believed, Macron’s bid for the centre-ground could pay off handsomely. But not everyone is convinced.

“He’s the perfect representative of the electorate in the big globalised cities,” the geographer Christophe Guilluy told Le Point magazine in January.

“But it’s the peripheries of France that will decide this presidential election.”