barbara got a flat tire and does not have a spare. she needs her car for work, so she goes to a business…

barbara got a flat tire and does not have a spare. she needs her car for work, so she goes to a business that offers payday loans in order to get the money to buy a new tire. she borrows $75 and plans to pay it back when she gets paid in 8 days. barbara is charged a fee of $15 and the term on her loan is 8 days. approximately what is the annual percentage rate on her loan?\na. 228%\nb. 487%\nc. 913%\nd. 973%

barbara got a flat tire and does not have a spare. she needs her car for work, so she goes to a business that offers payday loans in order to get the money to buy a new tire. she borrows $75 and plans to pay it back when she gets paid in 8 days. barbara is charged a fee of $15 and the term on her loan is 8 days. approximately what is the annual percentage rate on her loan?\na. 228%\nb. 487%\nc. 913%\nd. 973%

Answer

Answer:

c. 913%

Explanation:

Step1: Calculate the daily interest rate

The interest amount $I = 15$ and the principal $P=75$. The daily interest rate $r_d$ is calculated as $r_d=\frac{I}{P}$. So, $r_d=\frac{15}{75}=0.2$ or 20% per day.

Step2: Calculate the number of 8 - day periods in a year

There are 365 days in a year. The number of 8 - day periods $n=\frac{365}{8}\approx45.625$.

Step3: Calculate the annual interest rate

The annual interest rate $r_a$ is found by multiplying the daily interest rate by the number of 8 - day periods in a year. So, $r_a = r_d\times n=0.2\times45.625\times100% = 912.5%\approx913%$.