Question 1196452: Marina had a car accident, and the repair bill came to $900. She didn't have any emergency fund 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 $18 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 Theo(13342)   (Show Source):
You can put this solution on YOUR website! at simple interest, i = p * r * n
i = interest
p = principal
r = rate per time period
n = number of time periods
when i = .18 * 900 = 162 and n = 30 days, the formula becomes:
162 = 900 * r * 30
solve for r to get:
r = 162/(900 * 30) = .006 per day.
with 365 days per year, then i = 900 * .006 * 365 = 1971
the equivalent annual interest = 1971.
the equivalent annual interest rate = 1971/900 -1 = 1.19 = 119%.
an equivalent way of doing it is to make your time period years instead of days.
the formula becomes 162 = 900 * r * 30/365.
solve for r to get r = 162 / (900 * 30/365) = 2.19 - 1 = 1.19 = 119% per year.
either way, the answer comes out the same.
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