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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The most terrifying thing about Donald Trump's speech? What he didn't say

No politician uses official speeches to put across their most controversial ideas. But Donald Trump's are not hard to find. 

As Donald Trump took the podium on a cold Washington day to deliver his inauguration speech, the world held its breath. Viewers hunched over televisions or internet streaming services watched Trump mouth “thank you” to the camera, no doubt wondering how he could possibly live up to his deranged late-night Twitter persona. In newsrooms across America, reporters unsure when they might next get access to a president who seems to delight in denying them the right to ask questions got ready to parse his words for any clue as to what was to come. Some, deciding they couldn’t bear to watch, studiously busied themselves with other things.

But when the moment came, Trump’s speech was uncharacteristically professional – at least compared to his previous performances. The fractured, repetitive grammar that marks many of his off-the-cuff statements was missing, and so, too, were most of his most controversial policy ideas.

Trump told the crowd that his presidency would “determine the course of America, and the world, for many, many years to come” before expressing his gratefulness to President Barack Obama and Michelle Obama for their “gracious aid” during the transition. “They have been magnificent," Trump said, before leading applause of thanks from the crowd.

If this opening was innocent enough, however, it all changed in the next breath. The new president moved quickly to the “historic movement”, “the likes of which the world has never seen before”, that elected him President. Following the small-state rhetoric of his campaign, Trump promised to take power from the “establishment” and restore it to the American people. “This moment," he told them, “Is your moment. It belongs to you.”

A good deal of the speech was given over to re-iterating his nationalist positions while also making repeated references to the key issues – “Islamic terrorism” and families – that remain points of commonality within the fractured Republican GOP.

The loss of business to overseas producers was blamed for “destroying our jobs”. “Protection," Trump said, “Will lead to great strength." He promised to end what he called the “American carnage” caused by drugs and crime.

“From this day forward," Trump said, “It’s going to be only America first."

There was plenty in the speech, then, that should worry viewers, particularly if you read Trump’s promises to make America “unstoppable” so it can “win” again in light of his recent tweets about China

But it was the things Trump didn't mention that should worry us most. Trump, we know, doesn’t use official channels to communicate his most troubling ideas. From bizarre television interviews to his upsetting and offensive rallies and, of course, the infamous tweets, the new President is inclined to fling his thoughts into the world as and when he sees fit, not on the occasions when he’s required to address the nation (see, also, his anodyne acceptance speech).

It’s important to remember that Trump’s administration wins when it makes itself seem as innocent as possible. During the speech, I was reminded of my colleague Helen Lewis’ recent thoughts on the “gaslighter-in-chief”, reflecting on Trump’s lying claim that he never mocked a disabled reporter. “Now we can see," she wrote, “A false narrative being built in real time, tweet by tweet."

Saying things that are untrue isn’t the only way of lying – it is also possible to lie by omission.

There has been much discussion as to whether Trump will soften after he becomes president. All the things this speech did not mention were designed to keep us guessing about many of the President’s most controversial promises.

Trump did not mention his proposed ban on Muslims entering the US, nor the wall he insists he will erect between America and Mexico (which he maintains the latter will pay for). He maintained a polite coolness towards the former President and avoiding any discussion of alleged cuts to anti-domestic violence programs and abortion regulations. Why? Trump wanted to leave viewers unsure as to whether he actually intends to carry through on his election rhetoric.

To understand what Trump is capable of, therefore, it is best not to look to his speeches on a global stage, but to the promises he makes to his allies. So when the President’s personal website still insists he will build a wall, end catch-and-release, suspend immigration from “terror-prone regions” “where adequate screening cannot occur”; when, despite saying he understands only 3 per cent of Planned Parenthood services relate to abortion and that “millions” of women are helped by their cancer screening, he plans to defund Planned Parenthood; when the president says he will remove gun-free zones around schools “on his first day” - believe him.  

Stephanie Boland is digital assistant at the New Statesman. She tweets at @stephanieboland