Question 1173057
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