Question 1182569: A payday loan is a short-term loan that is repaid on the next payday, often by giving the lender electronic access to a personal checking account. Some states have statutes that regulate the fees that may be charged for payday loans. Suppose that, in a certain state, finance charges on a payday loan may not exceed 17.4% of the amount advanced.
Find the annual interest rate if $600 is borrowed for 8 days at the maximum allowable charge.
Round to the nearest percent as needed.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the loan is 600.
the finance charge is .174 * 600 = 104.4
that's for 8 days.
the annual charge at that rate for every 8 days would be 365/8*104.4 = 4763.25.
that would make the annual interest rate = 4763.25 / 600 = 7.93875 * 100 = 793.875%.
the formula for simple interest is i = p * r * t
i is the interest
p is the principal
r is the interest rate per time period
n is the number of time periods
the interest rate per time period is .174 for 8 days.
divide that by 8 to get an interest rate of .02175 each day.
multiply that by 365 to get an interest rate of 7.93875 each year.
the formula becomes i = 600 * 7.93875 * 1 = 4763.25
alternately, it can become i = 600 * .02175 * 365 = 4763.25
the first one uses the annual rate with a time period of 1 year.
the second one uses the daily rate with time period of 365 days.
it is assumed that one year is equal to 365 days.
the interest charge is the same.
the bottom line is that you are paying an exorbitant sum for interest on a pay day loan.
they are designed for short periods only.
the fly in the ointment is that there is no mention of how long the payday loan can be.
if it's 8 days, the maximum interest charge is 17.4%.
if it's 16 days, the maximum interest charge is still 17.4%.
it appears that the maximum interest charge will be 17.4% regardless of the length of the loan.
there may also be a law that a payday loan can only be so long, i.e. 7 or 14 days or 30 days, depending on the interval of pay.
all of these need to be taken into consideration.
based on this problem, without taking all of those things into consideration, i would bo with an equivalent annual rate of 793.875%.
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