Question

Roberta has $10,540 to invest. She plans to invest her money in certificates of deposit (CDs) that have 2.1% interest, a stock portfolio that makes 2.5% interest, and a savings account that has 1.5% interest. She would like to make $231.69 in annual interest from her investments. Also, to provide some risk security, she wants to invest a third of the amount she puts in the stock portfolio in the savings account. Let x be the amount invested in CDs, y be the amount invested in the stock portfolio, and z be the amount invested in the savings account. What is the amount Roberta invests in each type of investment?
The amount invested in CDs (x) is $....?

The amount invested in the stock portfolio (y) is $.....?

The amount invested in the savings account (z) is $....?

Answer 1

Answer:

The amount invested in CDs is  $1,340

The amount invested in the stock portafolio is $6,900

The amount invested in the saving accounts is $2,300

Step-by-step explanation:

Let

x ---->the amount invested in CDs at 2.1%

y ---> the amount invested in the stock portfolio at 2.5%

z ---> the amount invested in the savings account at 1.5%

$x+y+z=10,540$ ----> equation A

$z=\frac{1}{3}y$ ----> equation B

substitute equation B in equation A

$x+y+\frac{1}{3}y=10,540$

$x+\frac{4}{3}y=10,540$

$x=10,540-\frac{4}{3}y$ ----> equation C

we know that

The total interest earned by the three amount must be equal to $231.69

so

$0.021x+0.025y+0.015z=231.69$ ----> equation D

substitute equation B and equation C in equation D

$0.021(10,540-\frac{4}{3}y)+0.025y+0.015(\frac{1}{3}y)=231.69$

solve for y

$221.34-0.0315y+0.025y+0.005y=231.69$

$0.0015y=231.69-221.34$

$0.0015y=10.35$

$y=\ 6,900$

Find the value of x

$x=10,540-\frac{4}{3}(6,900)$

$x=\ 1,340$

Find the value of z

$z=\frac{1}{3}(6,900)$

$z=\ 2,300$