Question 1187129: Formulate a system of equations for the situation below and solve.
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 15%/year; medium-risk stocks, 10%/year; and low-risk stocks, 5%/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 $32,000/year on the total investment. (Assume that all the money available for investment is invested.)
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
"...the investment in low-risk stocks should be equal to the sum of the investments in the stocks of the other two categories."
That means half of the $400,000 should be invested in the low-risk stocks that return 5% interest. 5% interest on $200,000 is $10,000 interest.
So the return on the other $200,000 should be $32,000-$10,000 = $22,000.
$22,000 return on a $200,000 investment is a rate of 22/200 = 11/100 = 11%.
Here is a quick and easy way to finish the problem:
(1) Look at the three percentages 10, 11, and 15 on a number line and observe/calculate that 11% is 1/5 of the way from 10% to 15%.
(2) That means 1/5 of the remaining $200,000 should be invested at the higher (15%) rate.
1/5 of $200,000 is $40,000.
So...
ANSWER:
$200,000 at 5%
$40,000 at 15%
$160,000 at 10%
CHECK:
.05($200,000)+.15($40,000)+.10($160,000) = $10,000+$6000+$16,000 = $32,000
If a formal mathematical method for determining the distribution of the second $200,000 between the 10% and 15% return investments, you can do something like this:
x = amount invested at 15%
200,000-x = amount invested at 10%
The total interest from those two needs to be $22,000:
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