If you borrow \$10,000 at an annual interest rate of 8\% compounded semiannually, what is the amount of interest charged for the first 6 months?

• A. \$800
• B. \$200
• C. \$400
• D. \$500

Answer: (C)

Verified step by step guidance

1. Understand the problem: You are calculating the interest charged for the first 6 months on a loan of \$10,000 at an annual interest rate of 8%, compounded semiannually.
2. Identify the formula for calculating interest for a single compounding period: \( I = P \times r \), where \( I \) is the interest, \( P \) is the principal, and \( r \) is the interest rate per compounding period.
3. Determine the interest rate per compounding period: Since the annual interest rate is 8% and the interest is compounded semiannually, divide the annual rate by 2. \( r = \frac{8\%}{2} = 4\% \) or \( 0.04 \) in decimal form.
4. Substitute the values into the formula: \( I = 10,000 \times 0.04 \). This will give the interest charged for the first 6 months.
5. Perform the multiplication to find the interest amount. The result will be the interest charged for the first 6 months.