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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Theresa May could live to regret not putting Article 50 to a vote sooner

Today's Morning Call.

Theresa May will reveal her plan to Parliament, Downing Street has confirmed. They will seek to amend Labour's motion on Article 50 adding a note of support for the principle of triggering Article 50 by March 2017, in a bid to flush out the diehard Remainers.

Has the PM retreated under heavy fire or pulled off a clever gambit to take the wind out of Labour's sails while keeping her Brexit deal close to her chest? 

Well, as ever, you pays your money and you makes your choice. "May forced to reveal Brexit plan to head off Tory revolt" is the Guardian's splash. "PM caves in on plans for Brexit" is the i's take. "May goes into battle for Brexit" is the Telegraph's, while Ukip's Pravda aka the Express goes for "MPs to vote on EU exit today".

Who's right? Well, it's a bit of both. That the government has only conceded to reveal "a plan" might mean further banalities on a par with the PM's one-liner yesterday that she was seeking a "red white and blue Brexit" ie a special British deal. And they've been aided by a rare error by Labour's new star signing Keir Starmer. Hindsight is 20:20, but if he'd demanded a full-blown white paper the government would be in a trickier spot now. 

But make no mistake: the PM didn't want to be here. It's worth noting that if she had submitted Article 50 to a parliamentary vote at the start of the parliamentary year, when Labour's frontbench was still cobbled together from scotch-tape and Paul Flynn and the only opposition MP seemed to be Nicky Morgan, she'd have passed it by now - or, better still for the Tory party, she'd be in possession of a perfect excuse to reestablish the Conservative majority in the House of Lords. May's caution made her PM while her more reckless colleagues detonated - but she may have cause to regret her caution over the coming months and years.

PANNICK! AT THE SUPREME COURT

David Pannick, Gina Miller's barrister, has told the Supreme Court that it would be "quite extraordinary" if the government's case were upheld, as it would mean ministers could use prerogative powers to reduce a swathe of rights without parliamentary appeal. The case hinges on the question of whether or not triggering Article 50 represents a loss of rights, something only the legislature can do.  Jane Croft has the details in the FT 

SOMETHING OF A GAMBLE

Ministers are contemplating doing a deal with Nicola Sturgeon that would allow her to hold a second independence referendum, but only after Brexit is completed, Lindsay McIntosh reports in the Times. The right to hold a referendum is a reserved power. 

A BURKISH MOVE

Angela Merkel told a cheering crowd at the CDU conference that, where possible, the full-face veil should be banned in Germany. Although the remarks are being widely reported in the British press as a "U-Turn", Merkel has previously said the face veil is incompatible with integration and has called from them to be banned "where possible". In a boost for the Chancellor, Merkel was re-elected as party chairman with 89.5 per cent of the vote. Stefan Wagstyl has the story in the FT.

SOMEWHERE A CLOCK IS TICKING

Michael Barnier, the EU's chief Brexit negotiator, has reminded the United Kingdom that they will have just 15 to 18 months to negotiate the terms of exit when Article 50 is triggered, as the remaining time will be needed for the deal to secure legislative appeal.

LEN'S LAST STAND?

Len McCluskey has quit as general secretary of Unite in order to run for a third term, triggering a power struggle with big consequences for the Labour party. Though he starts as the frontrunner, he is more vulnerable now than he was in 2013. I write on his chances and possible opposition here.

AND NOW FOR SOMETHING COMPLETELY DIFFERENT

Emad asks if One Night Stand provides the most compelling account of sex and relationships in video games yet.

MUST READS

Theresa May is becoming adept at avoiding defeats says George

Liv Constable-Maxwell on what the Supreme Court protesters want

Theresa May risks becoming an accidental Europe wrecker, says Rafael Behr

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Stephen Bush is special correspondent at the New Statesman. His daily briefing, Morning Call, provides a quick and essential guide to British politics.