Question

A private investment club has $400,000 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 14%/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 $36,000/year on the total investment. (assume that all the money available for investment is invested.)

Answer 1

To arrive at an acceptable overall level of risk, the private investment club should invest $60,000 in high-risk stocks, $140,000 in medium-risk stocks, and $200,000 in low-risk stocks. This allocation will allow the club to achieve a return of $36,000 per year on a total investment of $400,000.

Step-by-step explanation:

To determine how much the club should invest in each type of stock, we need to first calculate the rate of return for each category of stock. Let's denote the amount invested in high-risk stocks as H, medium-risk stocks as M, and low-risk stocks as L. Given that the investment goal is to have a return of $36,000 per year, we can set up the following equation:

0.14H + 0.09M + 0.07L = 36000

Since the investment in low-risk stocks should be equal to the sum of the investments in the stocks of the other two categories, we have:

L = H + M

We also know that the total investment amount is $400,000:

H + M + L = 400000

Substituting L with H + M in the above equation, we get:

H + M + (H + M) = 400000

2H + 2M = 400000

Now we have a system of two equations with two variables. Solving these equations will give us the amounts to invest in each type of stock. Solving the second equation for H, we get:

H = (400000 - 2M) / 2

Substituting this value of H into the first equation, we obtain:

0.14((400000 - 2M) / 2) + 0.09M + 0.07((400000 - 2M) / 2) = 36000

Simplifying and solving for M gives us:

M = 140000

Substituting this value of M into the equation for H, we get:

H = (400000 - 280000) / 2 = 60000

Finally, substituting the values of H and M into the equation for L, we find:

L = H + M = 60000 + 140000 = 200000

Therefore, the club should invest $60,000 in high-risk stocks, $140,000 in medium-risk stocks, and $200,000 in low-risk stocks.

Answer 2

idk this one but i can help you find it if u want