A community center paid $\$432$ in simple interest after $3$ years on borrowed funds for new equipment. The interest rate was $4.5\%$ per year. What was the original amount borrowed?

• A. $\$2768$
• B. \$3200
• C. \$3632
• D. \$3500

Answer: (B)

Verified step by step guidance

1. Identify the formula for simple interest: \(\text{Simple Interest} = P \times r \times t\), where \(P\) is the principal (original amount borrowed), \(r\) is the annual interest rate (in decimal form), and \(t\) is the time in years.
2. Convert the interest rate from a percentage to a decimal by dividing by 100: \(4.5\% = \frac{4.5}{100} = 0.045\).
3. Substitute the known values into the simple interest formula: \(432 = P \times 0.045 \times 3\).
4. Simplify the right side by multiplying the interest rate and time: \(432 = P \times (0.045 \times 3)\).
5. Solve for \(P\) by dividing both sides of the equation by the product of the interest rate and time: \(P = \frac{432}{0.045 \times 3}\).