a radio commercial for a loan company​ states: "You only pay 28 cents a day for each​ $500 borrowed." If you borrow 2910$ for 151 ​days.

a) what amount will you​ repay?
b)what annual interest rate is the company actually​ charging? (Assume a​ 360-day year.)

1 answer

a) To find the total amount to repay, we need to calculate the number of $500 increments in the loan amount and then multiply it by the cost per day.

Number of $500 increments = loan amount / $500 = $2910 / $500 = 5.82 increments

Total cost per day = cost per day per $500 * number of $500 increments = 28 cents * 5.82 = $1.6296

Total amount to repay = total cost per day * number of days = $1.6296 * 151 = $246.27

b) To find the annual interest rate, we need to calculate the interest paid per year and divide it by the loan amount.

Interest paid per year = total amount to repay - loan amount = $246.27 - $2910 = -$2663.73

Annual interest rate = (interest paid per year / loan amount) * 100 = (-$2663.73 / $2910) * 100 = -91.54%

Since the interest rate is negative, it means that the company is actually refunding money to the borrower, which is not a realistic scenario.