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: \(I = P \times r \times t\), where \(I\) is the interest, \(P\) is the principal (amount borrowed), \(r\) is the annual interest rate (in decimal), and \(t\) is the time in years.
2. From the problem, note the values: interest \(I = 1350\), time \(t = 3\) years, and interest rate \(r = 9\% = 0.09\).
3. Substitute the known values into the formula: \(1350 = P \times 0.09 \times 3\).
4. Simplify the right side: \(1350 = P \times 0.27\).
5. Solve for \(P\) by dividing both sides by \(0.27\): \(P = \frac{1350}{0.27}\).