Deception by Numbers

Hey, want to borrow some money?

I can get you a really good rate on a short term loan, just 1% per day.  I know that sounds like it adds up after a while, but in the short term, 1% per day is hardly a lot.

Oh, and there may be a couple of little fees, just administrative stuff, nothing to worry about, the important thing  is that you need cash now, you don’t get paid until next week, and you don’t want to spend a lot of time reading paperwork or filling out forms.  1% a day isn’t all that much, and it’s worth it to you to get cash in hand.  So, what do you say?

I imagine many of you metaphorically backed away from me just as surely as if I were a used car dealer challenging you to find any rust on this fine automobile, but to a lot of people this kind of swift loan is very enticing.  That’s why, if you either watch telly in the middle of the day or record entire series of Burn Notice on your DVR, you’ve probably seem more than a few advertisements for places like and other similar services, offering what they call “short term advances”.  These kind of businesses have become very popular in the last few years, and they thrive for a number of reasons, but I’m going to focus on one in particular for this article:

People aren’t very good with numbers.

Actually, that’s a little unfair.  It’s more accurate to say that the equations encountered during this kind of loan transaction don’t feel intuitive, and often have end results that are a long way from what the average person might expect.

For example, let’s take that loan I offered you a minute ago, with an interest rate of one percent per day.  You won’t be taking this loan out for a full year, but if someone were to ask you to guess, what would you estimate the annual percentage rate on such a loan would be?  Don’t grab a calculator, just take an educated guess.

Some people would guess that the annual percentage rate would be 365%, as there are 365 days in a year and the rate is 1% per day.  Not a totally unreasonable guess, and while an APR of 365% is daylight robbery, it won’t bother someone so much if it’s just a short term loan and they know what they’re getting themselves into.

The problem is that a guess like this leaves out compound interest.  Basically, it assumes your daily interest is 1% of the initial amount.  Sadly, interest does not work like that.  Your interest rate is 1% of the amount owing, which is the sum of the amount you originally borrowed, and the interest you have already been charged.  I’m going to leave aside any administrative fees and so forth as they make the whole situation even more complicated to explain.

Put simply, if I loan you one pound, then your interest for day one is going to be 1 penny, meaning that at the end of the day, you owe £1.01.  THe next day, however, the amount of interest you owe goes up slightly, to 1.01 pennies, meaning the total you owe is £1.0201 rather than £1.02.  Doesn’t sound like much, does it?

Keep repeating this, however, and that tiny amount gets bigger.  A 20 day loan at 1% a day actually costs you a little more than 22% of your original loan amount.  50 days brings this up to 64% . Your interest rate for the loan passes 100% on day 70.  On day 365, the interest rate for your loan reaches a whacking 3,678%, more than ten times what you might have assumed it was.

Compound interest for a fixed interest rate causes what is called exponential growth, and as time passes it can lead to a tiny insignificant fraction becoming a huge and weighty sum, in a way that can confound people’s expectations.  American physics professor Albert Bartlett once stated that “The greatest shortcoming of the human race is our inability to understand the exponential function”, and this is true in areas as diverse as population growth, finance, and pyramid schemes.

When a company does short term loans, they are in part depending on the fact that people hear 1%, and see the amount they have to repay, and don’t look much deeper into what they are actually being charged.

Now, in fairness to Wonga and similar businesses, they don’t do long term loans.  They aren’t likely to expose a borrower to an interest rate in the high thousands, because they won’t be lending the money for that long.  This does not change the fact, though, that saying “The annual rate of interest is 360%” as Wonga do on their website ( ) is at best misleading and at worst dishonest.

Where you get onto shakier ground is where you look at the less reputable of these companies, those who make more money through borrowers defaulting on their loans than they do through payments being made.  Almost all short term loans agreements will have severe punitive consequences for defaulting on the loan.  To a point, this is understandable, and can be argued as both a deterrent to defaulters and a way of recouping costs from having to pursue a delinquent borrower.  However, you do have to wonder, if they were so concerned with deterring people who might default, why would they make it so easy to get the loan in the first place?  At a certain point, though, this moves from being a punitive action and becomes a moneyspinner in its own right.  This is certainly true for other forms of loan and credit.  Most credit cards will have what they refer to as a “default rate”, often double or more the original interest rate, which kicks in when a payment is missed, and is very hard for a borrower to appeal.

So, what can the individual consumer do about this kind of thing?  The simplest answer is just “don’t get these kind of loans”, but this sort of behaviour, and this sort of hidden complexity, is by no means limited to short term loans.  Deception by numbers happens with just about every area where someone thinks they can make money from the public, and aside from  changes in the way these things are regulated, there are a few things a consumer can do to stay alert to what they are being offered:

  1. Find out what the numbers are, and more importantly what the numbers mean.  You don’t have to bring a pocket calculator with you everywhere you go (although most of us have one on our phones these days), but you can insist that before you agree to buy anything much more financially complicated than a sandwich, you get a complete picture of what you are paying and what you are getting.  If it’s a loan, find out all the rates, all the fees, and get them put into a standard form.  If it’s a product, find out how it compares to the cost of similar items.
  2. Don’t sign anything on the spot.  Get the terms and conditions first.  Once you get them, shock the world by reading them.  Companies go out of their way to make this part as complicated as possible, and these days the standard credit card agreement is multiple pages of fine print type.  If you don’t want to read every word, at least skim the whole thing to find every point where a particular rate or condition is mentioned.

These days, especially with the rise of click-through end user license agreements in software, people routinely click they agree with long sets of terms and conditions that they have not even looked at.  I defy anyone reading this to tell me they have read the EULA for every piece of software they have installed.  However, when it comes to financial transactions, where you are agreeing to be liable for substantial penalties, you owe it to your bank account to be aware of what you are agreeing to.

In a way, the short term loan industry shows in miniature the two major forces that led to the financial crisis, with loans being turned into commodities, and financial products representing little more than bets on the value of other financial products.  On one side, you have a consumer thinking in the short term and accepting a fantastic offer they aren’t numerate enough to fully understand.  On the other side, you have a loan industry that will bury the truth in loan agreements, wrap it in bright colours and palatable numbers, and try to find ways to make money whether the borrower repays or not.  The loan happens where greed meets greed, neither side thinking of the possible consequences.

So, what do you say about that loan?  It’s only 1% per day…