Answer:
It is necessary to invest $5,000 in the 8% option
And, $15,000 in the 12% option
Step-by-step explanation:
Let’s begin by calculating the total expected return.
With an anticipated total return of 11%, the expected amount back is;
11/100 * 20,000 = $2,200
Let x represent the amount put into the 8% investment, and y represent the investment in the 12% option
From this, we have the equation;
x + y = 20,000 ••••••(i)
Now considering the interest portion;
The interest for the 8% portion is 8/100 * x
For the 12% part, it’s 12/100 * y
Thus, we express that as;
(8/100 * x) + (12/100 * y) = 2,200
Consolidating, we have;
8x/100 + 12y/100 = 2,200
Multiplying throughout by 100 gives us
8x + 12y = 220,000 ••••••(ii)
Next, we can solve this system of equations;
x + y = 20,000
8x + 12y = 220,000
Using i, we find x = 20,000 - y
Substituting into ii yields;
8(20,000-y) + 12y = 220,000
160,000-8y + 12y = 220,000
Combining yields 4y = 220,000 - 160,000
Thus, 4y = 60,000
So, y = 60,000/4
y = $15,000
From this, x can be calculated as follows:
x = 20,000 - y
x = 20,000 - 15,000
x = $5,000