Formulate a system of equations for the situation below and solve. The managemen
ID: 3141091 • Letter: F
Question
Formulate a system of equations for the situation below and solve. The management of a private investment club has a fund of $400,000 earmarked for 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 type of stock. (Assume that all of the money available for investment is invested. Round your answers to the nearest cent.) high-risk stocks $ medium-risk stocks $ low-risk stocks $Explanation / Answer
Solution:
Let the investment in high risk be $ x and in medium risk be $ y
therefore Investment in low risk = 2 ($ x + $ y)
Total investment = x + y + 2x + 2y = 400,000
3x + 3y = 400,000 or
x+y = 400,000/3 ;
x = 400,000/3 -y
Total return on investments is
.15x + .1y + .06(2x+2y) = 36,000
0.15x + 0.12x +0.1y + 0.12y = 36,000
0.27x + 0.32y = 36,000
Solve for x and y and we get
x = 400000/3
y = 0
Answer: Investement in High risk stocks = $ 400000/3
Investment in Medium y = $ 0
Investment in Low risk 2(x+y) = $ 800000/3