Sofia plans to buy a car. Her loan statement indicates she will pay $\$1,350$ in interest for a $3$-year loan at $9\%$ simple interest per year. How much did Sofia borrow for the car?

• A. \$5,000
• B. \$4,500
• C. \$15,000
• D. \$6,350

Answer: (A)

Verified step by step guidance

1. Identify the formula for simple interest, which is given by: \[\text{Interest} = P \times r \times t\] where \(P\) is the principal (amount borrowed), \(r\) is the annual interest rate (in decimal form), and \(t\) is the time in years.
2. From the problem, note the values: Interest = \$1,350\(, Time \)t = 3\( years, Interest rate \)r = 9\% = 0.09$ (convert percent to decimal by dividing by 100).
3. Substitute the known values into the simple interest formula: \[1,350 = P \times 0.09 \times 3\]
4. Simplify the right side by multiplying the interest rate and time: \[1,350 = P \times 0.27\]
5. To find the principal \(P\), divide both sides of the equation by 0.27: \[P = \frac{1,350}{0.27}\] This will give the amount Sofia borrowed for the car.