Let's help Abigail evaluate her investment in the stock of a technology company with the information given.
1. Determine the number of whole shares Abigail can buy:
Abigail has [tex]$5,000 to invest, but she needs to account for a commission fee of $[/tex]10. Therefore, the amount she can actually use to buy shares is:
[tex]\[
\$5000 - \$10 = \$4990
\][/tex]
The current share price of the stock is [tex]$1,706. To find out how many whole shares she can buy, we perform the following calculation:
\[
\text{Number of whole shares} = \left\lfloor \frac{4990}{1706} \right\rfloor = 2 \text{ shares}
\]
Abigail can buy 2 whole shares of the stock.
2. Calculate the remaining money after buying the shares:
To determine how much money she will have left, calculate the cost of the 2 shares and subtract it from $[/tex]4,990:
[tex]\[
\text{Cost of 2 shares} = 2 \times 1706 = 3412
\][/tex]
[tex]\[
\text{Remaining money} = 4990 - 3412 = 1578
\][/tex]
Abigail will have [tex]$1,578 remaining after buying the shares.
3. Determine the dividend yield:
The dividend rate given for each share is $[/tex]2.32 annually. To find the dividend yield, we use the following formula:
[tex]\[
\text{Dividend Yield} = \left( \frac{\text{Dividend rate}}{\text{Share price}} \right) \times 100
\][/tex]
[tex]\[
\text{Dividend Yield} = \left( \frac{2.32}{1706} \right) \times 100 \approx 0.136 \%
\][/tex]
The dividend yield of the stock is approximately [tex]$0.136 \%$[/tex], which is less than [tex]$1 \%$[/tex].
4. Calculate the annual dividends Abigail will receive in the first year:
The total amount of dividends Abigail will receive is calculated by multiplying the number of shares by the dividend rate:
[tex]\[
\text{Dividends received} = 2 \times 2.32 = 4.64
\][/tex]
Abigail will receive [tex]$4.64 in dividends in the first year.
Conclusion:
Given the information, Abigail can buy 2 whole shares of the stock with $[/tex]1,578 left over, and the dividend yield is approximately [tex]$0.136 \%$[/tex]. Since this yield is less than Abigail's threshold of [tex]$1 \%$[/tex], it is not recommended for her to invest in this particular stock if she wishes to reduce her risk with a dividend yield over [tex]$1 \%$[/tex].
