I'm going to disagree with the sibling responses here and agree with your premise - I actually think in some cases it's not fair to calculate APR for short term, low value loans. Here's why: There's a transaction cost with making a loan - paperwork, time, etc., and in many cases that transaction cost doesn't scale with the loan size.

Example to illustrate: Let's say I ask you for a personal loan. If I need $100,000 and I want to pay you back over a few years, let's say you charge me 5% APR. You write me a check and you can roughly count on the fact that I'm going to pay you ~$5,000 a year for the service. I get the money I need, you make a nice return, we're both happy.

Now let's say I need $100 for a week. If you charged me the same 5% APR, that means I pay you back about $100.096 next week. Is it worth it? Pretty good deal for me - I'm happy to get a week's usage of $100 and it only cost me a dime. Pretty bad deal for you - and in fact, I expect you wouldn't want to even do the deal. Not worth the risk!

So what do you charge me? What's it worth to hand me a $100 and hope you'll get it back in a week? $1? Still pretty low - and that's 52% APR! $5? Getting closer - now you can buy a beer or two at the bar next week. But that's 260%! $10? Now we're at 520% APR.

It doesn't really scale at low numbers.