Question

Compute the total and annual returns on the described investment.4 years after buying 50 shares of XYZ stock for $50 per share, you sell the stock for $3,500The total return is %? (Do not round until the final answer. Then round to one decimal place as needed.)

Answer 1

The investment consists of 50 shares for $50 each, thus the amount invested was 50 x $50 = $2,500.

After 4 years, the stock is sold for $3,500. This gives a total return of:

$\frac{3,500-2,500}{2,500}=\frac{1,000}{2,500}=0.4$

The total return is 0.4 x 100 = 40%

An annualized total return is the geometric average amount of money earned by an investment each year over a given time period.

Suppose the annual rate is r and it's compounded yearly for 4 years. Since the total return is 40%, the percentage, including the initial investment is 140% = 1.4, thus:

$(1+r)^4=1.4$

Applying 4th root:

$1+r=\sqrt[4]{1.4}=1.0877$

Solving for r:

r = 0.0877 = 8.77%

Rounding to one decimal: r = 8.8%