# Compound interest and loan sharks – MBA Learnings

We discussed a a segment on CBS regarding Pay Day loans in our accounting class. CBS discussed a Pay Day Loan organizations that charged a bi-weekly interest rate of 15%. They spoke about how outrageous this was as, in their estimation, this meant the lender was charging customers an interest rate of 400%. Now, let’s get into the numbers –

The first step is to spend a minute understanding compound interest. Every great personal finance book starts with requesting the reader to appreciate the beauty and power of compound interest. So, here goes – let’s imagine you have a principle amount of \$10 growing at 10% compound interest per year. That means –

At the end of year 1, you have interest of – (\$10 x 10%) = \$1
At the end of year 2, you have interest of – \$1 + (\$10 x 10%) + (\$1 x 10%) = \$2.1

That little snippet describes what makes compound interest special. In the first year, you earn \$1 on the initial \$10. But, in the second year, you not only earn the \$1 on the \$10, you also earn an additional \$0.1 on the \$1 you earned last year.

At the end of year 3, you have interest of – \$2.1 + (\$10 x 10%) + (\$2.1 x 10%)  = \$3.31
At the end of year 4, you have interest of – \$3.31 + (\$10 x 10%) + (\$3.31 x 10%) = \$4.64

So, over time, it keeps giving you returns on the interest you already have. Substitute these with much larger numbers and a long time period, and you’ll see how quickly compound interest can increase wealth. The formula for compound interest is P (1 + r)^n where P is the principal, r is the rate of interest and n is the number of time periods.

Let’s go back to the loan sharks now. The rate of interest is 15% and the time period is bi-weekly. There are 52 weeks in a year => 26 “bi-weekly” time periods. CBS’ calculation was 15*26 = 390% or around 400%. This equates to \$400 of interest for every \$100 in 1 year.

However, they’ve forgotten that the 15% interest is compounded. That means the lenders also charge the 15% on the interest to be repaid over time. This means we have to think of it in terms of compound interest. The real rate, therefore is (1 + r)^n or (1+0.15)^26 (assuming principal to be 1) = 37.86 or 3,786%

If you’ve ever wondered how loan sharks make money, that is how. For every \$100 loaned by a loan shark, they get around \$3,786 back in a year for a “15%” bi-weekly interest rate.

One final note – bankers have come under lots of criticism since the financial crisis. While the industry definitely deserves the sort of scrutiny it has been getting, there was commentary about whether life was better without banks. I think this example illustrates how critical banks are towards progress in society. If we’re complaining about a 20% interest on our credit cards, well, maybe we ought to speak to a loan shark..