The Management of a private investment club has a fund of $200,000 earmarked for

Question

The Management of a private investment 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 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 an average rate of return of 9% year on the total investment, determine how much the club should invest in each stock. (Assume all of the money available for investment is invested)

Explanation / Answer

Here is what is given: x = amount invested in high risk stocks y = amount invested in medium risk stocks z = amount invested in low risk stocks hence you have your system of equations: x + y + z = 200,000 0.15x + 0.1y + 0.06z = 0.09(200,000) 2(x + y)= z and so (x, y, z) = ($66,666,67, $0, $133,333.33)

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