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.

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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 Fire Brigades Union reaffiliates to Labour - what does it mean?

Any union rejoining Labour will be welcomed by most in the party - but the impact on the party's internal politics will be smaller than you think.

The Fire Brigades Union (FBU) has voted to reaffiliate to the Labour party, in what is seen as a boost to Jeremy Corbyn. What does it mean for Labour’s internal politics?

Firstly, technically, the FBU has never affliated before as they are notionally part of the civil service - however, following the firefighters' strike in 2004, they decisively broke with Labour.

The main impact will be felt on the floor of Labour party conference. Although the FBU’s membership – at around 38,000 – is too small to have a material effect on the outcome of votes themselves, it will change the tenor of the motions put before party conference.

The FBU’s leadership is not only to the left of most unions in the Trades Union Congress (TUC), it is more inclined to bring motions relating to foreign affairs than other unions with similar politics (it is more internationalist in focus than, say, the PCS, another union that may affiliate due to Corbyn’s leadership). Motions on Israel/Palestine, the nuclear deterrent, and other issues, will find more support from FBU delegates than it has from other affiliated trade unions.

In terms of the balance of power between the affiliated unions themselves, the FBU’s re-entry into Labour politics is unlikely to be much of a gamechanger. Trade union positions, elected by trade union delegates at conference, are unlikely to be moved leftwards by the reaffiliation of the FBU. Unite, the GMB, Unison and Usdaw are all large enough to all-but-guarantee themselves a seat around the NEC. Community, a small centrist union, has already lost its place on the NEC in favour of the bakers’ union, which is more aligned to Tom Watson than Jeremy Corbyn.

Matt Wrack, the FBU’s General Secretary, will be a genuine ally to Corbyn and John McDonnell. Len McCluskey and Dave Prentis were both bounced into endorsing Corbyn by their executives and did so less than wholeheartedly. Tim Roache, the newly-elected General Secretary of the GMB, has publicly supported Corbyn but is seen as a more moderate voice at the TUC. Only Dave Ward of the Communication Workers’ Union, who lent staff and resources to both Corbyn’s campaign team and to the parliamentary staff of Corbyn and McDonnell, is truly on side.

The impact of reaffiliation may be felt more keenly in local parties. The FBU’s membership looks small in real terms compared Unite and Unison have memberships of over a million, while the GMB and Usdaw are around the half-a-million mark, but is much more impressive when you consider that there are just 48,000 firefighters in Britain. This may make them more likely to participate in internal elections than other affiliated trade unionists, just 60,000 of whom voted in the Labour leadership election in 2015. However, it is worth noting that it is statistically unlikely most firefighters are Corbynites - those that are will mostly have already joined themselves. The affiliation, while a morale boost for many in the Labour party, is unlikely to prove as significant to the direction of the party as the outcome of Unison’s general secretary election or the struggle for power at the top of Unite in 2018. 

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