Question

Formulate but do not solve the problem. The management of a private investment club has a fund of $250,000 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 amount of money invested in low risk stocks is to be twice the sum of the amount invested 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.) _ = 250,000 _= z _= 22,500.

Answer 1

Answer:

In this problem it is necessary to propose and solve the following system of equations:

0.15 X + 0.10 Y + 0.06 Z = 0.09 * 250,000       (1)

X + Y + Z = 250,000                                          (2)

Z = 2 ( X + Y )                                                      (3)

Being the variables

X = $ invested in high-risk stocks

Y = $ invested in medium-risk stocks

Z = $ invested in low-risk stocks

Explanation:

Equation (1) tells us that the sum of the amounts invested in each type of action multiplied by its expected return, is equal to the return that is desired for the entire investment (9% of $ 250,000).

Equation (2) says that the sum of the investments must be equal to the money available to invest.

Equation (3) requires that money invested in low-risk shares (Z) be equal to twice the amount invested in the other two categories.