Question 1190050: Marina had an accident with her car and the repair bill came to $900. She didn’t have any emergency fund money and no extra money in her monthly budget, so she ended up borrowing from a pay-day loan company. As long as she can pay the loan back at the end of the 30 day period she won’t be charged any interest, technically. However, she did have to pay an $17 processing fee per $100 that she borrowed.
If she were to consider the processing fee to represent interest paid in her formula, what would she discover to be the annual interest rate she was charged on her short term loan?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Assuming she pays back the money entirely before the 30 day period is up, then the only extra fee is the $17 per $100 mentioned.
She borrows $900 which means there are 900/100 = 9 lots of the 17. In other words, 9*17 = 153 is the processing fee paid on top of the $900 she needs to pay back.
That $153 covers 30 days.
If we're dealing with a 360 day year (some, if not most, banking formulas rely on this convention), then that's 30/360 = 1/12 of the year. So 12*153 = 1836 would cover the entire year if this rate is kept up.
Then divide this over the original amount borrowed
1836/900 = 2.04 = 204%
The annual rate is 204%
It's very common to have payday loans with such high APR. If anything, this is probably on the low end of the scale.
If your teacher wants you to use a 365 day year, then the multiplier 365/30 will scale the $153 up to 153*(365/30) = 1861.50
Then we can say
1861.50/900 = 2.068 = 206.8% approximately
which isn't too far from the 204% APR calculated earlier.
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