Question

The management of a private investment club has a fund of $270,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high risk (x), medium risk (y), and low risk (z). Management estimates that high risk stocks will have a rate of return of 15%/year; medium risk stocks, 10%/year; and low risk stocks, 6%/year. The investment in low risk stocks is to be twice the sum of the investments in stocks of the other two categories. If the investment goal is to have a rate of return of 9% on the total investment, determine how much the club should invest in each type of stock. (Assume that all the money available for investment is invested.)

Answer 1

Investment in stock

X=90,000

Y=0

Z=180,000

Explanation:

As we know, the total investment is 270,000. It means: x+y+z=270,000

And z=2(x+y) as investment in z is double the sum of other two investments.

So x+y+2(x+y)=270,000. Which gives

X+y=90,000. ... Eq 1

So, z= 2(x+y)= 180,000

And we also know, 15%x+10%y+6%z=270,000*9%

Putting value of z:

15%x+10%y+6%(2(x+y))=24,300.

15%x+10%y+6%(180,000)=24,300

15%x+10%y=24,300-10,800

15%x+10%y=13,500

15x+10y=1,350,000 ....eq 2

Solving eq 1 and eq 2 to get:

X=90,000

Y=0