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 paid, \(P\) 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 \(I = 1350\), time \(t = 3\) years, and interest rate \(r = 9\% = 0.09\) (convert percent to decimal by dividing by 100).
3. Substitute the known values into the simple interest formula: \(1350 = P \times 0.09 \times 3\).
4. Simplify the right side by multiplying the rate and time: \(1350 = P \times 0.27\).
5. Solve for \(P\) by dividing both sides of the equation by \$0.27$: \(P = \frac{1350}{0.27}\). This will give the amount Sofia borrowed.