What is the annual rate of return (to the nearest percent) earned on a \$1,000 investment that grows to \$1,800 in six years? (Assume interest is compounded annually.)

• A. 9%
• B. 10%
• C. 11%
• D. 8%

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the formula for calculating the annual rate of return when interest is compounded annually. The formula is: \( FV = PV \times (1 + r)^t \), where \( FV \) is the future value, \( PV \) is the present value, \( r \) is the annual rate of return, and \( t \) is the time in years.
2. Step 2: Substitute the given values into the formula. Here, \( FV = 1800 \), \( PV = 1000 \), and \( t = 6 \). The equation becomes: \( 1800 = 1000 \times (1 + r)^6 \).
3. Step 3: Isolate \( (1 + r)^6 \) by dividing both sides of the equation by \( 1000 \). This simplifies to: \( (1 + r)^6 = \frac{1800}{1000} \).
4. Step 4: Simplify \( \frac{1800}{1000} \) to \( 1.8 \). The equation now becomes: \( (1 + r)^6 = 1.8 \).
5. Step 5: Solve for \( r \) by taking the sixth root (or raising both sides to the power of \( \frac{1}{6} \)) and then subtracting 1. The equation becomes: \( r = (1.8)^{\frac{1}{6}} - 1 \).