Question

Friendly's quick loans, inc., offers you "$4.10 for $5.10 or i knock on your door." this means you get $4.10 today and repay $5.10 when you get your paycheck in one week (or else). if you were brave enough to ask, what apr would friendly's say you were paying?

Answer 1

1268% APR  
First, let's see what interest is charged over a 1 week period. 
(5.10 - 4.10)/ 4.10 = 1.00/4.10 = 0.2439 = 24.39%  
So we have 24.39% for 1 week. But APR stands for Annual Percentage Rate. And since there's 52 weeks in a year, we need to multiply that weekly percentage rate by 52. So: 
24.39% * 52 = 1268.28%  
Ouch, usury at it's greatest. You can get loans from Friendly's at the low low rate of only 1268% APR. I'd suggest going elsewhere for your financial needs.

Answer 2

If it costs $5.10 to get $4.10 from Friendly's then the loanee would pay about 24% which is a pretty high interest rate and presumably the interest rate would decrease with a higher amount loaned as on a larger amount the actual amount of interest earned would still be significant with a lower interest rate.