Question 8 4 pts 5 Details Lynne needs to borrow $\$ 9250$ for home repairs. She obtains a loan from her grandmother for 28 months at a simple annual interest rate of $9.2 \%$. How much will Lynne pay back to her grandmother? Be sure to clearly show your work on your paper! \$ Round to the nearest cent.

Step 1 ：Lynne needs to borrow $9250 for home repairs. She obtains a loan from her grandmother for 28 months at a simple annual interest rate of 9.2%.

Step 2 ：First, we need to convert the time from months to years. So, \( T = \frac{28}{12} = 2.33 \) years.

Step 3 ：Next, we calculate the interest using the formula \( I = PRT \), where \( P \) is the principal amount, \( R \) is the rate of interest, and \( T \) is the time. Substituting the given values, we get \( I = 9250 \times 0.092 \times 2.33 = 1985.67 \).

Step 4 ：Finally, we calculate the total amount to be paid back, which is the sum of the principal amount and the interest. So, \( total = P + I = 9250 + 1985.67 = 11235.67 \).

Step 5 ：The total amount Lynne will pay back to her grandmother is $11235.67 when rounded to the nearest cent.

Step 6 ：Final Answer: \(\boxed{11235.67}\).