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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Will Jeremy Corbyn stand down if Labour loses the general election?

Defeat at the polls might not be the end of Corbyn’s leadership.

The latest polls suggest that Labour is headed for heavy defeat in the June general election. Usually a general election loss would be the trigger for a leader to quit: Michael Foot, Gordon Brown and Ed Miliband all stood down after their first defeat, although Neil Kinnock saw out two losses before resigning in 1992.

It’s possible, if unlikely, that Corbyn could become prime minister. If that prospect doesn’t materialise, however, the question is: will Corbyn follow the majority of his predecessors and resign, or will he hang on in office?

Will Corbyn stand down? The rules

There is no formal process for the parliamentary Labour party to oust its leader, as it discovered in the 2016 leadership challenge. Even after a majority of his MPs had voted no confidence in him, Corbyn stayed on, ultimately winning his second leadership contest after it was decided that the current leader should be automatically included on the ballot.

This year’s conference will vote on to reform the leadership selection process that would make it easier for a left-wing candidate to get on the ballot (nicknamed the “McDonnell amendment” by centrists): Corbyn could be waiting for this motion to pass before he resigns.

Will Corbyn stand down? The membership

Corbyn’s support in the membership is still strong. Without an equally compelling candidate to put before the party, Corbyn’s opponents in the PLP are unlikely to initiate another leadership battle they’re likely to lose.

That said, a general election loss could change that. Polling from March suggests that half of Labour members wanted Corbyn to stand down either immediately or before the general election.

Will Corbyn stand down? The rumours

Sources close to Corbyn have said that he might not stand down, even if he leads Labour to a crushing defeat this June. They mention Kinnock’s survival after the 1987 general election as a precedent (although at the 1987 election, Labour did gain seats).

Will Corbyn stand down? The verdict

Given his struggles to manage his own MPs and the example of other leaders, it would be remarkable if Corbyn did not stand down should Labour lose the general election. However, staying on after a vote of no-confidence in 2016 was also remarkable, and the mooted changes to the leadership election process give him a reason to hold on until September in order to secure a left-wing succession.

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