Paul has $20,000 to invest. His intent is to earn 11% interest on his investment. He can invest part of his money at 8% interest

Question

2 months ago

13

and part at 12% interest. How much does Paul need to invest in each option to make get a total 11% return on his $20,000?

1 answer:

Leona [12.6K] · Answer 1 · 2026-03-06T22:11:36+03:00

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