Multiple Choice
What is the future value of \$1 invested today at an annual interest rate of \(r\) for \(n\) periods, compounded once per period?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
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
Verified step by step guidance1
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.
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.
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.
Substitute the values into the formula: \( I = 10,000 \times 0.04 \). This will give the interest charged for the first 6 months.
Perform the multiplication to find the interest amount. The result will be the interest charged for the first 6 months.
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