An investor is thinking about buying some shares of a company at $ 75 a share. She expects the stock to rise to $ 115 a share over the next 3 years. During that time, she also expects to receive annual dividends at $ 4 a share. Assuming that the future value and the dividends it pays hold up, what rate of return can she expect to earn on this investment?
To calculate the rate of return on an investment, you can use the formula for compound interest. In this case, we need to calculate the total future value of the investment and then determine the rate of return.
First, let's calculate the future value of the investment after 3 years. The initial investment is $75, and the stock is expected to rise to $115 per share. So the capital gain per share is $115 - $75 = $40.
To find the total future value, we need to consider both the capital gain and the dividends. The capital gain will be $40 multiplied by the number of shares bought. The dividend is mentioned as "$4 per share annually," so over 3 years, it will be $4 multiplied by the number of shares bought, and further multiplied by the number of years (3). Let's assume the number of shares bought is x.
Total future value = (Capital gain per share x Number of shares x Number of years) + (Dividend per share x Number of shares x Number of years)
Total future value = ($40 x x x 3) + ($4 x x x 3)
Now, let's calculate the rate of return using the formula:
Rate of return = (Total future value - Initial investment) / Initial investment
Substituting the values we calculated:
Rate of return = ((($40 x x x 3) + ($4 x x x 3)) - $75) / $75
Unfortunately, without knowing the number of shares bought (x), we cannot provide an exact rate of return. The rate of return will vary depending on the number of shares purchased.