Answer:
In the 8% option , $5,000 should be invested
In the 12% option, $15,000 should be invested
Step-by-step explanation:
Let’s start with the total return.
Since the total return expected is 11%, the amount expected to be returned will be;
11/100 * 20,000 = $2,200
Now, let the amount invested at 8% interest be $x while the amount invested at 12% interest be $y
Mathematically;
x + y = 20,000 ••••••(i)
Now let’s work with the interest part;
On the 8% part, amount of interest expected is 8/100 * x
on the 12% part, amount of interest expected is 12/100 * x
8% of $x + 12% of $y = 2,200
Writing this fully mathematically, we have;
(8/100 * x) + (12/100 * y) = 2,200
8x/100 + 12y/100 = 2,200
Multiply through by 100
8x + 12y = 220,000 ••••••(ii)
Now we have two equations to solve simultaneously;
x + y = 20,000
8x + 12y = 220,000
From i, x = 20,000-y
Substitute this into ii
8(20,000-y) + 12y = 220,000
160,000-8y + 12y = 220,000
4y = 220,000 - 160,000
4y = 60,000
y = 60,000/4
y = $15,000
x = 20,000 -y
x = 20,000 - 15,000
x = $5,000
