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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Why are boundary changes bad for Labour?

New boundaries, a smaller House of Commons and the shift to individual electoral registration all tilt the electoral battlefield further towards the Conservatives. Why?

The government has confirmed it will push ahead with plans to reduce the House of Commons to 600 seats from 650.  Why is that such bad news for the Labour Party? 

The damage is twofold. The switch to individual electoral registration will hurt Labour more than its rivals. . Constituency boundaries in Britain are drawn on registered electors, not by population - the average seat has around 70,000 voters but a population of 90,000, although there are significant variations within that. On the whole, at present, Labour MPs tend to have seats with fewer voters than their Conservative counterparts. These changes were halted by the Liberal Democrats in the coalition years but are now back on course.

The new, 600-member constituencies will all but eliminate those variations on mainland Britain, although the Isle of Wight, and the Scottish island constituencies will remain special cases. The net effect will be to reduce the number of Labour seats - and to make the remaining seats more marginal. (Of the 50 seats that would have been eradicated had the 2013 review taken place, 35 were held by Labour, including deputy leader Tom Watson's seat of West Bromwich East.)

Why will Labour seats become more marginal? For the most part, as seats expand, they will take on increasing numbers of suburban and rural voters, who tend to vote Conservative. The city of Leicester is a good example: currently the city sends three Labour MPs to Westminster, each with large majorities. Under boundary changes, all three could become more marginal as they take on more wards from the surrounding county. Liz Kendall's Leicester West seat is likely to have a particularly large influx of Tory voters, turning the seat - a Labour stronghold since 1945 - into a marginal. 

The pattern is fairly consistent throughout the United Kingdom - Labour safe seats either vanishing or becoming marginal or even Tory seats. On Merseyside, three seats - Frank Field's Birkenhead, a Labour seat since 1950, and two marginal Labour held seats, Wirral South and Wirral West - will become two: a safe Labour seat, and a safe Conservative seat on the Wirral. Lillian Greenwood, the Shadow Transport Secretary, would see her Nottingham seat take more of the Nottinghamshire countryside, becoming a Conservative-held marginal. 

The traffic - at least in the 2013 review - was not entirely one-way. Jane Ellison, the Tory MP for Battersea, would find herself fighting a seat with a notional Labour majority of just under 3,000, as opposed to her current majority of close to 8,000. 

But the net effect of the boundary review and the shrinking of the size of the House of Commons would be to the advantage of the Conservatives. If the 2015 election had been held using the 2013 boundaries, the Tories would have a majority of 22 – and Labour would have just 216 seats against 232 now.

It may be, however, that Labour dodges a bullet – because while the boundary changes would have given the Conservatives a bigger majority, they would have significantly fewer MPs – down to 311 from 330, a loss of 19 members of Parliament. Although the whips are attempting to steady the nerves of backbenchers about the potential loss of their seats, that the number of Conservative MPs who face involuntary retirement due to boundary changes is bigger than the party’s parliamentary majority may force a U-Turn.

That said, Labour’s relatively weak electoral showing may calm jittery Tory MPs. Two months into Ed Miliband’s leadership, Labour averaged 39 per cent in the polls. They got 31 per cent of the vote in 2015. Two months into Tony Blair’s leadership, Labour were on 53 per cent of the vote. They got 43 per cent of the vote. A month and a half into Jeremy Corbyn’s leadership, Labour is on 31 per cent of the vote.  A Blair-style drop of ten points would see the Tories net 388 seats under the new boundaries, with Labour on 131. A smaller Miliband-style drop would give the Conservatives 364, and leave Labour with 153 MPs.  

On Labour’s current trajectory, Tory MPs who lose out due to boundary changes may feel comfortable in their chances of picking up a seat elsewhere. 

Stephen Bush is editor of the Staggers, the New Statesman’s political blog. He usually writes about politics.