Formulate a system of equations for the situation below and solve. A private inv

Question

Formulate a system of equations for the situation below and solve.

A private investment club has $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, 9%/year; and low-risk stocks, 7%/year. The members have decided that the investment in low-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $20,800/year on the total investment. (Assume that all the money available for investment is invested.)

Explanation / Answer

Let the amount invested be H, M and L.

H+M+L = 200,000

L=H+M

So we get:

2H+2M =200000 -----(1)

0.15H+0.09M+0.07L = 28000

0.22H + 0.16M = 28000 -----(2)

Solving equation (1) and (2), we get:

0.22 x (100,000 – M) +0.16M = 28000

22000 -0.22M +0.16M =28000

M= -60,000

L=100,000

H= 200000+60000-100000

    = 160000

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