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.)

Question

Mathematics

Martin Middleton

25 February, 18:50

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.)

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Iliana · Answer 1

Investment in stock

X=90,000

Y=0

Z=180,000

Step-by-step 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