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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Empty highs: why throwaway plastic goes hand in hand with bankrupt consumerism

We are in the throes of a terrible addiction to stuff.

A University of California study revealed this week that mankind has produced more than nine billion tonnes of plastic since the 1950s, with almost all of it ending up in landfill or the ocean. With the terrible effects of our decades-long addiction to throwaway packaging becoming increasingly apparent, it’s clear that a fresh approach is needed.

In April 2010, David Cameron set out his vision for Britain in the Conservative Party’s manifesto. Keen to show that the Tories had turned away from the "I’m Alright Jack" individualism of the 1980s, Cameron sought to fashion a softer, more inclusive brand.

The good society, Cameron argued, embraced much higher levels of personal, professional, civic and corporate responsibility. There was such a thing as society, and we’d all do well to talk to our neighbours a bit more. The Big Society, however, was roundly derided as a smokescreen for an aggressive tightening of the Government purse strings. And on the advice of his 2015 election fixer Lynton Crosby, Cameron later dropped it in favour of well-worn lines about economic security and jobs.   

While most would argue that the Big Society failed to amount to much, Cameron was at least right about one thing. We are happiest when we are part of something bigger than ourselves. No matter how much the credit card companies try to convince us otherwise, mindless individualism won’t make us nearly as contented as we’re led to believe by big conglomerates.

By any measure, we are in the throes of a terrible addiction to stuff. As a nation, we have run up unsecured debts of more than £350bn, which works out at £13,000 per household. Fuelled by a toxic mix of readily available credit and interest rates at historic lows, we cripple ourselves financially to feel the empty high derived from acquiring yet more stuff.

Purchasing has become a leisure pursuit, ensuring the rate at which we acquire new stuff exceeds the rate at which we can find somewhere to put it. Burdened with ever increasing amounts of stuff, consumers are forced to outsource their storage. The UK didn’t have a self-storage industry 30 years ago, but now it is the largest in Europe.

With the personal debt mountain soaring, we’d all do well to realise that we will never have enough of something we don’t need.

The growth of rampant consumerism has coincided with an explosion in demand for single-use plastic. Like the superfluous possessions we acquire, throwaway plastic packaging helps satisfy our desire to get exactly what we want without having any thought for the long-term consequences. Plastic packaging is easy and convenient, but ultimately, will do us immense harm.

In 1950, close to 1.5 million tonnes of plastic was produced globally. Today, the figure stands at more than 320 million tonnes. The vast majority of our plastic waste either ends up in landfill or the ocean, and our failure to kick the plastic habit has put is in the ludicrous position where there is set to be more plastic than fish in global seas by 2050.

There is also growing evidence that our penchant for endless throwaway plastic might be storing up serious health problems for our children later down the line. According to a University of Ghent study published earlier this year, British seafood eaters risk ingesting up to 11,000 pieces of plastic each year. The report followed UN warnings last year that cancer-causing chemicals from plastic are becoming increasingly present in the food chain.

Something must give. Unsustainable as our reliance on fast credit to finance ever more stuff, our addiction to plastic packaging is storing up serious problems for future generations. The instant gratification society, high on the dopamine rush that fades so quickly after acquiring yet another material asset, is doomed unless decisive action is forthcoming.

So what is to be done? The 2016 US documentary Minimalism points to a smarter way forward. Minimalism follows the lives of ordinary people who have shunned the rat race in favour of a simpler life with less stuff and less stress. The most poignant bit of the film features ex-broker AJ Leon recounting how he chose to forgo the glamour and riches of Wall Street for a simpler life. After a meteoric rise to the top of his profession, Leon decided to jack it all in for a more fulfilling existence.

While challenging the view that to be a citizen is to be a consumer is easier said than done, there are small changes that we can enact today that will make a huge difference. We simply have no choice but to dramatically reduce the amount of plastic that we can consume. If we don’t, we may soon have to contend with the ocean being home to more plastic than fish.

Like plastic, our bloated consumer culture is a disaster waiting to happen. There must be a better way.

Sian Sutherland is co-founder of campaign group A Plastic Planet which is campaigning for a plastic free-aisle in supermarkets.

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