Questions: Question 28 (2 points) You purchased shares in NewWeb.com for 9800. Three years later, you sold them for 6500. What was your annual return on this investment? Give the answer in percent notation rounded to the nearest tenth of a percent.

Solution Steps

To find the annual return on the investment, we need to calculate the compound annual growth rate (CAGR). The formula for CAGR is:

\[ \text{CAGR} = \left( \frac{\text{Ending Value}}{\text{Beginning Value}} \right)^{\frac{1}{n}} - 1 \]

where \( n \) is the number of years. We will then convert this to a percentage and round to the nearest tenth of a percent.

We have the following values for the investment:

• Beginning Value: \( \$9800 \)
• Ending Value: \( \$6500 \)
• Number of Years: \( n = 3 \)

The formula for the Compound Annual Growth Rate (CAGR) is given by:

\[ \text{CAGR} = \left( \frac{\text{Ending Value}}{\text{Beginning Value}} \right)^{\frac{1}{n}} - 1 \]

Substituting the values:

\[ \text{CAGR} = \left( \frac{6500}{9800} \right)^{\frac{1}{3}} - 1 \]

Calculating the fraction:

\[ \frac{6500}{9800} \approx 0.6633 \]

Now, applying the exponent:

\[ \text{CAGR} \approx (0.6633)^{\frac{1}{3}} - 1 \approx -0.1279 \]

To express the CAGR as a percentage:

\[ \text{Annual Return} \approx -0.1279 \times 100 \approx -12.79 \]

Rounding to the nearest tenth of a percent gives:

\[ \text{Annual Return} \approx -12.8\% \]

Final Answer