Questions: Compute the total and annual returns on the described investment. Six years after buying 150 shares of XYZ stock for 80 per share, you sell the stock for 18,700. The total return is %. (Do not round until the final answer. Then round to one decimal place as needed.)

Compute the total and annual returns on the described investment. Six years after buying 150 shares of XYZ stock for 80 per share, you sell the stock for 18,700.

The total return is %.
(Do not round until the final answer. Then round to one decimal place as needed.)

Transcript text: Compute the total and annual returns on the described investment. Six years after buying 150 shares of $X Y Z$ stock for $\$ 80$ per share, you sell the stock for $\$ 18,700$. The total return is $\square$ \%. (Do not round until the final answer. Then round to one decimal place as needed.)

Solution

Solution Steps

Step 1: Calculate the Initial Investment Cost

The initial investment cost is calculated as the number of shares bought multiplied by the purchase price per share.

\[ \text{Initial Cost} = N \times P = 150 \times 80 = 12000 \]

Step 2: Calculate the Total Return

The total return is calculated as the percentage difference between the total selling price and the initial investment cost.

\[ \text{Total Return \%} = \left( \frac{S - \text{Initial Cost}}{\text{Initial Cost}} \right) \times 100 = \left( \frac{18700 - 12000}{12000} \right) \times 100 = 55.8\% \]

Step 3: Calculate the Annual Return

The annual return is calculated using the formula for the compound annual growth rate (CAGR).

\[ \text{Annual Return \%} = \left( \left( \frac{S}{\text{Initial Cost}} \right)^{\frac{1}{T}} - 1 \right) \times 100 = \left( \left( \frac{18700}{12000} \right)^{\frac{1}{T}} - 1 \right) \times 100 = 7.7\% \]