A $10$-year government bond paid $5.8\%$ simple interest per year. Over the $10$ years, the bond earned $\$4,640$ in interest. What was the principal of the bond?

• A. $\$3360$
• B. $\$7000$
• C. $\$8000$
• D. \$80000

Answer: (C)

Verified step by step guidance

1. Identify the formula for simple interest: \(I = P \times r \times t\), where \(I\) is the interest earned, \(P\) is the principal amount, \(r\) is the annual interest rate (in decimal form), and \(t\) is the time in years.
2. Convert the given interest rate from a percentage to a decimal by dividing by 100: \(5.8\% = \frac{5.8}{100} = 0.058\).
3. Substitute the known values into the simple interest formula: \(4640 = P \times 0.058 \times 10\).
4. Simplify the right side of the equation by multiplying the interest rate and time: \(4640 = P \times 0.58\).
5. Solve for the principal \(P\) by dividing both sides of the equation by \(0.58\): \(P = \frac{4640}{0.58}\).