My Notes 4 166 points 06 Submissions Used Formulate but do n

My Notes 4. -1.66 points 0/6 Submissions Used Formulate but do not solve the problem. The management of a private investment club has a fund of $180,000 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.) 180,000 16,200

Solution

Total Investment = $ 180,000

Let the investment in high Risk be I_H

Let the investment in medium Risk be I_M

Let the investment in low Risk be I_L

therefore

             I_H +I_M +I_L = 180000                    (1)

Investment in low risk twice the sum of other two

therefore

                            2(I_H +I_M) = I_L              (2)

From (1) and (2) we can find I_z = 120000

and I_H + I_M = 60000

Investment goal is to have 9% return on total investment

therefore total return = 180000 x 9/100   = 16200

returm from low risk = I_H X 6/100 = 120000 x 6 /100 = 7200

Return from the other two = 16200 - 7200 = 9000

I_H X 15/100 + I_M X 10/100 = 9000                 (3)

drom these equations we can find each investment