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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Is Yvette Cooper surging?

The bookmakers and Westminster are in a flurry. Is Yvette Cooper going to win after all? I'm not convinced. 

Is Yvette Cooper surging? The bookmakers have cut her odds, making her the second favourite after Jeremy Corbyn, and Westminster – and Labour more generally – is abuzz with chatter that it will be her, not Corbyn, who becomes leader on September 12. Are they right? A couple of thoughts:

I wouldn’t trust the bookmakers’ odds as far as I could throw them

When Jeremy Corbyn first entered the race his odds were at 100 to 1. When he secured the endorsement of Unite, Britain’s trade union, his odds were tied with Liz Kendall, who nobody – not even her closest allies – now believes will win the Labour leadership. When I first tipped the Islington North MP for the top job, his odds were still at 3 to 1.

Remember bookmakers aren’t trying to predict the future, they’re trying to turn a profit. (As are experienced betters – when Cooper’s odds were long, it was good sense to chuck some money on there, just to secure a win-win scenario. I wouldn’t be surprised if Burnham’s odds improve a bit as some people hedge for a surprise win for the shadow health secretary, too.)

I still don’t think that there is a plausible path to victory for Yvette Cooper

There is a lively debate playing out – much of it in on The Staggers – about which one of Cooper or Burnham is best-placed to stop Corbyn. Team Cooper say that their data shows that their candidate is the one to stop Corbyn. Team Burnham, unsurprisingly, say the reverse. But Team Kendall, the mayoral campaigns, and the Corbyn team also believe that it is Burnham, not Cooper, who can stop Corbyn.

They think that the shadow health secretary is a “bad bank”: full of second preferences for Corbyn. One senior Blairite, who loathes Burnham with a passion, told me that “only Andy can stop Corbyn, it’s as simple as that”.

I haven’t seen a complete breakdown of every CLP nomination – but I have seen around 40, and they support that argument. Luke Akehurst, a cheerleader for Cooper, published figures that support the “bad bank” theory as well.   Both YouGov polls show a larger pool of Corbyn second preferences among Burnham’s votes than Cooper’s.

But it doesn’t matter, because Andy Burnham can’t make the final round anyway

The “bad bank” row, while souring relations between Burnhamettes and Cooperinos even further, is interesting but academic.  Either Jeremy Corbyn will win outright or he will face Cooper in the final round. If Liz Kendall is eliminated, her second preferences will go to Cooper by an overwhelming margin.

Yes, large numbers of Kendall-supporting MPs are throwing their weight behind Burnham. But Kendall’s supporters are overwhelmingly giving their second preferences to Cooper regardless. My estimate, from both looking at CLP nominations and speaking to party members, is that around 80 to 90 per cent of Kendall’s second preferences will go to Cooper. Burnham’s gaffes – his “when it’s time” remark about Labour having a woman leader, that he appears to have a clapometer instead of a moral compass – have discredited him in him the eyes of many. While Burnham has shrunk, Cooper has grown. And for others, who can’t distinguish between Burnham and Cooper, they’d prefer to have “a crap woman rather than another crap man” in the words of one.

This holds even for Kendall backers who believe that Burnham is a bad bank. A repeated refrain from her supporters is that they simply couldn’t bring themselves to give Burnham their 2nd preference over Cooper. One senior insider, who has been telling his friends that they have to opt for Burnham over Cooper, told me that “faced with my own paper, I can’t vote for that man”.

Interventions from past leaders fall on deaf ears

A lot has happened to change the Labour party in recent years, but one often neglected aspect is this: the Labour right has lost two elections on the bounce. Yes, Ed Miliband may have rejected most of New Labour’s legacy and approach, but he was still a protégé of Gordon Brown and included figures like Rachel Reeves, Ed Balls and Jim Murphy in his shadow cabinet.  Yvette Cooper and Andy Burnham were senior figures during both defeats. And the same MPs who are now warning that Corbyn will doom the Labour Party to defeat were, just months ago, saying that Miliband was destined for Downing Street and only five years ago were saying that Gordon Brown was going to stay there.

Labour members don’t trust the press

A sizeable number of Labour party activists believe that the media is against them and will always have it in for them. They are not listening to articles about Jeremy Corbyn’s past associations or reading analyses of why Labour lost. Those big, gamechanging moments in the last month? Didn’t change anything.

100,000 people didn’t join the Labour party on deadline day to vote against Jeremy Corbyn

On the last day of registration, so many people tried to register to vote in the Labour leadership election that they broke the website. They weren’t doing so on the off-chance that the day after, Yvette Cooper would deliver the speech of her life. Yes, some of those sign-ups were duplicates, and 3,000 of them have been “purged”.  That still leaves an overwhelmingly large number of sign-ups who are going to go for Corbyn.

It doesn’t look as if anyone is turning off Corbyn

Yes, Sky News’ self-selecting poll is not representative of anything other than enthusiasm. But, equally, if Yvette Cooper is really going to beat Jeremy Corbyn, surely, surely, she wouldn’t be in third place behind Liz Kendall according to Sky’s post-debate poll. Surely she wouldn’t have been the winner according to just 6.1 per cent of viewers against Corbyn’s 80.7 per cent. 

Stephen Bush is editor of the Staggers, the New Statesman’s political blog.