30 Oct 2008

## Why "APR" on Small, Short Loans Can Be Misleading

On a recent MR thread, Tyler Cowen was pointing to ridiculously high APRs on certain consumer loans, and speculating on the reason for their existence. My good friend Silas (aka Person) was the first to provide the solution, namely that people were paying 35 pounds for convenience; they weren’t taking out a loan with 222% interest.

I seconded Silas’ explanation, relating how I would agonize over different credit card offers etc. until I realized I was wasting a half hour stressing on something that would mean a difference of \$65 either way. And regardless of where that number was coming from, I was getting way too worked up over \$65.

But a third commenter really sealed the deal with this scenario from his blog:

In his breathless expose of the payday loan industry [Dec. 3, 2005], the Citizen asks, “would you pay 61 trillion percent interest on a loan?” Well, in some cases, yes, I would, and you probably would too.

I’m in line at the coffee shop at work, and realize I forgot to bring my wallet. I turn to my co-worker. If he can lend me \$20, I tell him, I’ll buy him a \$2 coffee. He agrees. The next morning, after I’ve been to the bank machine, I pay him back his \$20.

Clearly, my friend is an exploitative loan shark. With compounding, the twenty-four-hour loan cost me an annual interest rate of about 128 quadrillion percent — 128,330,558,031,335,269,* to be more exact. That’s 2,000 times higher than even the payday loan operators.

And it’s a good thing I didn’t stop by the bank machine until the next day. There’s a bank machine between the coffee shop and my desk. If I had paid back the loan in five minutes, rather than 24 hours, the effective interest rate would be much higher. Much, much higher — it would have 4,354 digits!

* In the comments he caught a mistake; he had calculated the rate based on a loan of \$20, but actually it was a net loan of \$18 because of the coffee.