Mathematics, philosophy, code, travel and everything in between. More about me…

I write about

English | Czech
Choose your language. I write in English, but I translate many of my articles to Czech as well. Zvolte si jazyk. Píšu anglicky, ale řadu svých článků překládám i do češtiny.

Loansharking in practice: SMS loan analysis

You might have noticed certain companies offering so-called SMS loans: short-term, low-principal, nearly instant loans you can get simply by sending a text message. The offer sounds alluring. Are you squeezed for cash a week before the payday? No problem, just text us, we send you $200 now and you’ll repay $221 next week. But how good these offers really are? Have you heard of a 133,550% interest rate before? Let me show you…

I’ve come across one such Czech provider today, They offer loans of 1,000 – 10,000 CZK (roughly $52 – $523) for between 1 and 30 days. Let’s take their current rates (as of 10/8/2012) and see what a bargain they are.

First impressions are important

First, a crude but telling measure: let’s see the ratio of interest to principal, for different loan maturities (X axis) and principals (individual curves).

plot of interest/principal ratios

What’s particularly interesting is the huge drop of interest on 15-day loans of 1,000 and 2,000 CZK. Guess what… when you first come to the default loan offer is, wait for it, 2,000 CZK for 15 days. Your first impression will therefore tend to be “hey, that’s not all that expensive”. What a coincidence.


Nominal APR

That was entertaining, now let’s get serious. We’ll calculate the APR (Annual Percentage Rate) of the loans. APR is an interest rate calculated to facilitate comparison between loans with different maturity.

We’ll calculate nominal APR first. It does not reflect the true cost of borrowing exactly, but it’s easy to understand even without any knowledge of financial mathematics. Nominal APR tells us how expensive would a loan be if it were taken repeatedly over the whole year. A 1-day loan would be taken out 365 times, a 2-day loan 182.5 times and so on. The formula therefore is

<$$ \text{Nominal APR} = \frac{\text{interest}}{\text{principal}} \cdot \frac{365}{\text{maturity}}. $$>

plot of nominal APR

Wow! Now that’s a pretty picture. Note that the values on the vertical axis are in percent. So if you were to take out a 1-day loan every day of the year, you would pay roughly 2,500% – 3,150% of interest. On the other hand, a year of 30-day loans would cost you only 250% – 330%.

Effective APR, yield curves

And now the most accurate measure for comparing loans. Effective APR is the implied interest rate compounded for one year. I used the formula defined by European Union Directive 98/7/EC which in our case reduces to

<$$ \text{Effective APR} = \left(1 + \frac{\text{interest}}{\text{principal}}\right)^{\frac{365}{\text{maturity}}} - 1. $$>

For maturities less than five days this formula yields rates in excess of millions percent which makes it rather hard to plot. So these are rates between 5 and 30 days.

plot of effective APR

And here’s a beautiful detail, from 14 to 30 days.

plot of effective APR


Just in case you didn’t get it, I was being really sarcastic. When doing these calculations I was alternating between incredulous laughter and the urge to throw up. Interest rates of this kind are nothing else than loansharking and daylight robbery.

Companies like Crediton target people lacking basic financial education. Unfavorable rates are also often accompanied by harsh sanctions in the case of problematic repayment. I find such business models despicable. But Crediton is obviously not the only company doing this. Not so long ago I noticed an SMS loan provider that ran a debt collection agency on the side, thus covering its entire food chain…

So please, think and don’t become a prey. The laws of finance are merciless. When somebody lends you money quickly and easily without much ado, be assured that they have taken care of their profitability and survival… in some way.

October 7, MMXII — Finance.