Final answer:
Mel's annualized return on the ABC stock is 96%, calculated by finding the simple return from the buying and selling prices, then adjusting it for the six-month holding period to express it on an annual basis.
Step-by-step explanation:
To calculate Mel's annualized return on the stock, we need to consider the price she bought the stock for, the price she sold it for, and the time period she held onto the stock. Mel bought ABC stock for $21 per share and sold it for $29.4 per share six months later. The return in dollar terms is the selling price minus the buying price, which is calculated as $29.4 - $21 = $8.4 per share. However, since she only held the stock for six months, we need to annualize this return to understand it in yearly terms.
To annualize the return, we use the following formula:
Annualized Return = (1 + (Simple Return))^(1 / (Holding Period in Years)) - 1
First, calculate the simple return which is the price change divided by the initial price: $8.4 / $21 = 0.4 or 40%. Then we convert the holding period into years. Since six months is half a year, the holding period in years is 0.5. Now we plug the values into the annualized return formula:
Annualized Return = (1 + 0.4)^(1 / 0.5) - 1
Solving for the annualized return will give us:
Annualized Return = (1.4)^(2) - 1 = 1.96 - 1 = 0.96 or 96%
Thus, Mel's annualized return on her investment in ABC stock is 96%.