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Question 1173057: Calculate the daily and annual rate of interest charged on a payday loan of $400 if the interest charged was $35 when it was paid back 6 days later.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the payday loan was for 400 dollars.
the charge was 35 when the loan is paid back 6 days later.
these types of loans are usually assumed to be simple interest type loans.
the formula for a simple interest loan would be:
i = p * r * t
i is the interest
p is the principal
r is the interest rate per time period
t is the number of time periods.
in this problem:
i = 35
p = 400
t = 6 days
the formula becomes:
35 = 400 * r * 6
solve for r to get:
r = 35 / (400 * 6) = .0145833333 per day.
confirm this value of r is correct by replacing r in the formula used to get:
35 = 400 * .0145833333 * 6 = 35, confirming the value of r is good.
that value for r is per day.
assuming a year is equal to 365 days, then r per year would be equal to 365 * .0145833333 = 5.32291666 = 532.291666%.
that's over 500% interest rate per year.
your solution is:
the daily interest rate charge is .0145833333 = 1.45833333% per day.
the yearly interest rate charge would be .0145833333 * 365 = 5.322916667 = 532.2916667% per year.
rounded your percentages to 2 decimal places and you get:
interest rate charge is 1.46% per day.
interest rate charge is 532.29% per year
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