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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The footie is back. Three weeks in and what have we learned so far?

Barcleys, boots and big names... the Prem is back.

Another season, another reason for making whoopee cushions and giving them to Spurs fans to cheer them up during the long winter afternoons ahead. What have we learned so far?

Big names are vital. Just ask the manager of the Man United shop. The arrival of Schneiderlin and Schweinsteiger has done wonders for the sale of repro tops and they’ve run out of letters. Benedict Cumberbatch, please join Carlisle United. They’re desperate for some extra income.

Beards are still in. The whole Prem is bristling with them, the skinniest, weediest player convinced he’s Andrea Pirlo. Even my young friend and neighbour Ed Miliband has grown a beard, according to his holiday snaps. Sign him.

Boots Not always had my best specs on, but here and abroad I detect a new form of bootee creeping in – slightly higher on the ankle, not heavy-plated as in the old days but very light, probably made from the bums of newborn babies.

Barclays Still driving me mad. Now it’s screaming from the perimeter boards that it’s “Championing the true Spirit of the Game”. What the hell does that mean? Thank God this is its last season as proud sponsor of the Prem.

Pitches Some groundsmen have clearly been on the weeds. How else can you explain the Stoke pitch suddenly having concentric circles, while Southampton and Portsmouth have acquired tartan stripes? Go easy on the mowers, chaps. Footballers find it hard enough to pass in straight lines.

Strips Have you seen the Everton third kit top? Like a cheap market-stall T-shirt, but the colour, my dears, the colour is gorgeous – it’s Thames green. Yes, the very same we painted our front door back in the Seventies. The whole street copied, then le toot middle classes everywhere.

Scott Spedding Which international team do you think he plays for? I switched on the telly to find it was rugby, heard his name and thought, goodo, must be Scotland, come on, Scotland. Turned out to be the England-France game. Hmm, must be a member of that famous Cumbrian family, the Speddings from Mirehouse, where Tennyson imagined King Arthur’s Excalibur coming out the lake. Blow me, Scott Spedding turns out to be a Frenchman. Though he only acquired French citizenship last year, having been born and bred in South Africa. What’s in a name, eh?

Footballers are just so last season. Wayne Rooney and Harry Kane can’t score. The really good ones won’t come here – all we get is the crocks, the elderly, the bench-warmers, yet still we look to them to be our saviour. Oh my God, let’s hope we sign Falcao, he’s a genius, will make all the difference, so prayed all the Man United fans. Hold on: Chelsea fans. I’ve forgotten now where he went. They seek him here, they seek him there, is he alive or on the stairs, who feckin’ cares?

John Stones of Everton – brilliant season so far, now he is a genius, the solution to all of Chelsea’s problems, the heir to John Terry, captain of England for decades. Once he gets out of short trousers and learns to tie his own laces . . .

Managers are the real interest. So refreshing to have three young British managers in the Prem – Alex Neil at Norwich (34), Eddie Howe at Bournemouth (37) and that old hand at Swansea, Garry Monk, (36). Young Master Howe looks like a ball boy. Or a tea boy.

Mourinho is, of course, the main attraction. He has given us the best start to any of his seasons on this planet. Can you ever take your eyes off him? That handsome hooded look, that sarcastic sneer, the imperious hand in the air – and in his hair – all those languages, he’s so clearly brilliant, and yet, like many clever people, often lacking in common sense. How could he come down so heavily on Eva Carneiro, his Chelsea doctor? Just because you’re losing? Yes, José has been the best fun so far – plus Chelsea’s poor start. God, please don’t let him fall out with Abramovich. José, we need you.

Hunter Davies is a journalist, broadcaster and profilic author perhaps best known for writing about the Beatles. He is an ardent Tottenham fan and writes a regular column on football for the New Statesman.

This article first appeared in the 27 August 2015 issue of the New Statesman, Isis and the new barbarism