Question

A private investment club has $300,000 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 return rate of 15%; medium-risk stocks, 10%; and low-risk stocks, 6%. 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 $30,000 on the total investment. (Assume that all the money available for investment is invested. Let x, y, and z denote the amount, in dollars, invested in high-, medium-, and low-risk stocks, respectively.)

Answer 1

Investment in low risk=$150,000

Investment in medium risk =$30,000

Investment in high risk=$120,000

Step-by-step explanation:

✓We can denote the investment in high risk as $x

✓ We can denote the investment medium risk as $y

✓We can denote the investment in low risk as($x + $y)

The summation of the investment = x + y +( x + y )= $300,000

If we add the like-terms together we have,

2x + 2y = $300,000

If we divide the both sides by 2, we have

x+y = 150,000

If we make "x" as subject of the formula, we have

x =150,000 -y •••••••••••eqn(**)

Total return on investments is

0.15x +0.10y +0 .06(x+y) = $30,000••••••••••••••••••••••••••••eqn(#)

Substitute for x from eqn(**) into equation (#)

0.15(150,000 -y) + 0.10y + 0.06(150,000-y +y) = 30,000

22500-0.15y+0.10y+9000= 30,000

0.05y=1500

y=1500/0.05

y=30,000

Recall, x =150,000 -y

Then

x = 150,000 - 30,000 = 120,000

y=30,000

x=120,000

Investment in low risk = x + y

= 30,000+120,000= 150,000

Hence, the investment in high risk

is $120,000, the investment medium risk is $30,000 and the investment in low risk is $ 150,000.