Question

a radio commercial for a loan company states "You only pay 29 a day for each $500 borrowed." If you borrow $2,439 for 278 days, what amount will you repay, and what annual interest rate is the company actually charging? (Assume a 360-day year.) a. Amount you repay = $(Round to two decimal places.) b. Annual interest rate = []% (Round to four decimal places.)

Answer 1

The amount to repay for a loan of $2,439 is $141.76, and the annual interest rate charged by the company is 17.46%.

Step-by-step explanation:

a) To calculate the amount you will repay, you need to determine the daily cost of borrowing $500.

According to the radio commercial, you only pay $29 per day for each $500 borrowed.

So, to calculate the amount you will repay for a loan of $2,439, you divide $2,439 by $500 to find out how many $500 increments you are borrowing.

$2,439 / $500

= 4.878.

Then, you multiply that by the daily cost of $29 to find out how much you will repay per day.

4.878 x $29

= $141.762.

b) To calculate the annual interest rate, you can use the formula:

Interest = Principal x Rate x Time

Given that the loan term is 278 days (less than a year), we can calculate the interest amount:

$2,439 = $500 x Rate x 278

Dividing both sides of the equation by $500 x 278 gives us:

Rate = $2,439 / ($500 x 278)

= 0.1746

To convert this to a percentage, we multiply by 100:

Rate = 0.1746 x 100

= 17.46%