Question 1187129
<br>
"...the investment in low-risk stocks should be equal to the sum of the investments in the stocks of the other two categories."<br>
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.<br>
So the return on the other $200,000 should be $32,000-$10,000 = $22,000.<br>
$22,000 return on a $200,000 investment is a rate of 22/200 = 11/100 = 11%.<br>
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.<br>
1/5 of $200,000 is $40,000.<br>
So...<br>
ANSWER:
$200,000 at 5%
$40,000 at 15%
$160,000 at 10%<br>
CHECK:
.05($200,000)+.15($40,000)+.10($160,000) = $10,000+$6000+$16,000 = $32,000<br>
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:<br>
x = amount invested at 15%
200,000-x = amount invested at 10%<br>
The total interest from those two needs to be $22,000:<br>
{{{.15(x)+.10(200000-x)=22000}}}
{{{.15x+20000-.10x=22000}}}
{{{.05x=2000}}}
{{{x = 2000/.05 = 40000}}}<br>