Question

A group of investors decides to invest $500,000 in the stocks of three companies. Company D sells for $60 a share and has an expected growth of 16% per year. Company E sells for $80 per share and has an expected growth of 12% per year. Company F sells for $30 a share and has an expected growth of 9% per year. The group plans to buy four times as many shares of company F as of company E. If the group's goal is 13.68% growth per year, how many shares of each stock should the investors buy?

Answer 1

Let x be the number of shares of D, y be the number of shares of E, and z be the number of shares of F. We get the following equations.

 

60x+80y+30z = 500,000

 

0.16(60x)+0.12(80y) + 0.09(30z) = 0.1368(60x + 80y+ 30z)

 

z=4y

 

Simplify the first equation. 6x+8y+3z=50,000

 

Simplify the second equation.

 

9.6x+9.6y+2.7z = 8.208x + 10.944y+ 4.104z

 

1.392x-1.344y-1.404z= 0

 

1392x-1344y-1404z=0

 

116x-112y-117z=0

second equation= 116x-112y-117z=0

first equation=6x+8y+3z=50,000