Jacob purchased 110 shares of stock in a computer company at $92.63 per share and Rae purchased 45 shares of stock in a different computer company for $87.45 per share. After holding the stock for two years, Jacob sold his for a total of $11,120.53, and Rae sold hers for a total of $4,192.10. Which person had a higher ROI and by how much?
A. Jacob: 9.1% more
B. Rae: 6.5% more
C. Jacob: 2.6% more
D. Rae: 2.6% more
I think C? I'm not sure.
I agree.
To calculate the ROI (Return on Investment), we need to find the percentage increase or decrease in the value of the investment.
Step 1: Calculate the initial investment for Jacob:
Initial investment for Jacob = Number of shares purchased * Cost per share
Initial investment for Jacob = 110 shares * $92.63 per share
Initial investment for Jacob = $10,188.30
Step 2: Calculate the ROI for Jacob:
ROI for Jacob = (Final value of investment - Initial investment) / Initial investment * 100
ROI for Jacob = ($11,120.53 - $10,188.30) / $10,188.30 * 100
ROI for Jacob = $932.23 / $10,188.30 * 100
ROI for Jacob = 9.14%
Step 3: Calculate the initial investment for Rae:
Initial investment for Rae = Number of shares purchased * Cost per share
Initial investment for Rae = 45 shares * $87.45 per share
Initial investment for Rae = $3,935.25
Step 4: Calculate the ROI for Rae:
ROI for Rae = (Final value of investment - Initial investment) / Initial investment * 100
ROI for Rae = ($4,192.10 - $3,935.25) / $3,935.25 * 100
ROI for Rae = $256.85 / $3,935.25 * 100
ROI for Rae = 6.52%
Comparing the ROI values, we see that Jacob's ROI is 9.14% and Rae's ROI is 6.52%. Therefore, Jacob had a higher ROI, with a difference of 2.62%.
So, the correct answer is:
C. Jacob: 2.6% more
To determine the return on investment (ROI) for both Jacob and Rae, we need to calculate the difference between the selling price and the total cost of purchasing the shares, and then divide that difference by the total cost of purchasing the shares.
For Jacob:
Jacob purchased 110 shares at $92.63 per share, so the total cost of his shares was 110 * $92.63 = $10,189.30.
The difference between the selling price and the total cost of purchasing the shares is $11,120.53 - $10,189.30 = $931.23.
The ROI for Jacob is $931.23 / $10,189.30 = 0.091, or 9.1%.
For Rae:
Rae purchased 45 shares at $87.45 per share, so the total cost of her shares was 45 * $87.45 = $3,935.25.
The difference between the selling price and the total cost of purchasing the shares is $4,192.10 - $3,935.25 = $256.85.
The ROI for Rae is $256.85 / $3,935.25 = 0.065, or 6.5%.
Comparing the two ROIs, it can be seen that Jacob had a higher ROI. To calculate the difference in their ROIs, subtract the ROI for Rae from the ROI for Jacob:
Jacob's ROI - Rae's ROI = 0.091 - 0.065 = 0.026, or 2.6%.
Therefore, the correct answer is option C. Jacob had a ROI that was 2.6% more than Rae's ROI.