Given:
percent of dividend = 6%
percent of interest = 9%
Total annual interest = $ 660
Let the amount invested in both stocks be x and y.
Annual interest on 6% dividend gives:
[tex]\begin{gathered} =\text{ }\frac{6}{100}\text{ }\times\text{ x} \\ =\text{ 0.06x} \end{gathered}[/tex]Annual interest on 9% interest rate:
[tex]\begin{gathered} =\text{ }\frac{9}{100\text{ }}\times\text{ y} \\ =\text{ 0.09y} \end{gathered}[/tex]The total annual interest is $ 660. We can write:
[tex]0.06x\text{ + 0.09y =660}[/tex]We are given that Nelson divided his investment in half. This implies:
[tex]x\text{ = y}[/tex]Substituting, we have:
[tex]\begin{gathered} 0.06x\text{ + 0.09x = 660} \\ 0.15x\text{ = 660} \end{gathered}[/tex]Divide both sides by 0.15:
[tex]\begin{gathered} \frac{0.15x}{0.15}\text{ = }\frac{660}{0.15} \\ x\text{ = 4400} \end{gathered}[/tex]Hence, the amount Nelson has invested:
[tex]\begin{gathered} x\text{ = y = 4400} \\ \text{Amount invested = 4400 + 4400} \\ =\text{ 8800} \end{gathered}[/tex]Answer:
Nelson has $4400 invested in each investment
