Compound interest and loan sharks | MBA Learnings

First-year student Rohan Rajiv is blogging once a week about important lessons he is learning at Kellogg. Read more of his posts here.

We recently discussed a segment on CBS regarding payday loans in our accounting class. CBS discussed a payday loan organization that charged a biweekly interest rate of 15%. They spoke about how outrageous this was. In their estimation, this meant the lender was charging customers an interest rate of 400%.

But let’s look at the numbers.

The first step is to spend a minute understanding compound interest. Every great personal finance book starts with requesting the reader appreciate the beauty and power of compound interest. So, here we go.

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 $0.10 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 biweekly. There are 52 weeks in a year, so 26 “biweekly” 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% biweekly interest rate.

One final note. Bankers have come under lots of criticism because of 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 toward 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.

Rohan Rajiv is a first-year student in Kellogg’s Full-Time Two-Year Program. Prior to Kellogg he worked at a-connect serving clients on consulting projects across 14 countries in Europe, Asia, Australia and South America. He blogs a learning every day, including his MBA Learnings series, on www.ALearningaDay.com.