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)

In order to obtain a return of 9% per year, we need to invest $133,333.333 in low risk investments, $0 in mid risk investment and $66,666.666 in high risk investment.

Step-by-step explanation:

2/3 of the $200,000 for investment should go to low risk, and the other third to mid risk and high risk. Lets call X the amount that goes into high risk, then the amount that goes to mid risk is 200,000/3 - X.

If we want a 9% of return for the total investment, then we should end with $200,000 * 1.09 = $218,000. We can compute what money we expect to end the year with in terms of X and then obtain the value of X.

We end the year with

200,000 * 1.06 * 2/3 + (200,000/3 - X) * 1.09 + X * 1.15 = 214000 + X * (1.15 - 1.09) = 214000 + X * 0.06

Since we want this amount to be equal to 218000, then

214000+X * 0.06 = 218000

X*0.06 = 218000-214000 = 4000

X = 4000/0.06 = 66,666.666 = 200,000/3

Thus, we are not investing in the mid risk category.

In order to obtain a return of 9% per year, we need to invest $200,000/3 = $133,333.333 in low risk investments, $0 in mid risk investment and $66,666.666 in high risk investment.