Question

An executive invests $28000, some at 8% and the rest at 6% annual interest. If he receive annual return of $2000 how much is invested at each rate?

Answer 1

Answer:

$16,000 at 8% annual interest.

$12,000 at 6% annual interest.

Step-by-step explanation:

Let x be amount invested at a rate of 8% annual interest and y be the amount invested at a rate of 6% annual interest.

We have been given that an executive invests $28000, some at 8% and the rest at 6% annual interest. We can represent this information as:

$x+y=28,000...(1)$

We are also given that he received annual return of $2000. We can represent this information as:

$(\frac{8}{100})x+(\frac{6}{100})y=2,000...(2)$

$0.08x+0.06y=2,000...(2)$

We will use substitution method to solve our system of equations. From equation (1) we will get,

$x=28,000-y$

Substituting this value in equation (2) we will get,

$0.08(28,000-y)+0.06y=2,000$

$2240-0.08y+0.06y=2,000$

$2240-2240-0.08y+0.06y=2,000-2240$

$-0.08y+0.06y=2,000-2240$

$-0.02y=-240$

$\frac{-0.02y}{-0.02}=\frac{-240}{-0.02}$

$y=12,000$

Therefore, the executive has invested $12,000 at a rate of 6% annual interest.

Upon substituting y=12,000 in equation (1) we will get,

$x+12,000=28,000$

$x+12,000-12,000=28,000-12,000$

$x=16,000$

Therefore, the executive has invested $16,000 at a rate of 8% annual interest.

Answer 2

Answer:

Amount invested at 8% interest rate = $16000

Amount invested at 6% interest rate = $12000

Step-by-step explanation:

Total amount invested = $28000

Let amount invested with 8% interest rate be $x

Then amount invested at 6% interest rate = 28000 - x

Now, Total return = Return from 8% interest rate + Return from 6% interest rate

⇒ 2000 = 8% (in decimal form) × amount invested + 6%(in decimal form) × Amount invested

⇒ 2000 = 0.08 × x + 0.06 × (28000 - x)

⇒ 2000 = 0.02·x + 1680

⇒ x = 16000

Hence, Amount invested at 8% interest rate = $16000

And, Amount invested at 6% interest rate = 28000 - 16000

                                                                         = $12000