Question

ulate but do not solve the problem t club has a fund of $200,000 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, medium-risk, and low-risk. Management estimates that high-risk stocks will have a rate of return of 16%/year, medium risk stocks, 9%/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 categ es, the investment goal is to have an average rate of return of 9% year 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. Let x, y, and z denote the amount, in dolars, invested in high-, medium-, and low-risk stocks, respectively.) 200,000 .09(200,000)

Answer 1

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Let the investment in high risk be $x and in medium risk be $y

Investment in low risk = 2($x + $y)

Total investment = x + y +2( x + y )= 200000

x+y+2x+2y=200000

3x + 3y = 200000

3(x+y)=200000

x+y = 66667  

x = 66667 -y

Total return on investments is

0.16x + 0.09y +0.06(x+y) = 200000*9%

Substitute for x

0.16(66667 -y) +0 .09y + .06(66667-y +y) = 18000

10,667-0.16y +0 .09y +4,000 = 18000

0.07y = 3,333

y = 47614

x = 66667 - 47614 = 19,053

Investment in low risk = 2(x + y )=2(19053*47614)

=133,334