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 $....?

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calculista calculista · Answer 1 · 2020-01-15T13:26:30+01:00

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%

[tex]x+y+z=10,540[/tex] ----> equation A

[tex]z=\frac{1}{3}y[/tex] ----> equation B

substitute equation B in equation A

[tex]x+y+\frac{1}{3}y=10,540[/tex]

[tex]x+\frac{4}{3}y=10,540[/tex]

[tex]x=10,540-\frac{4}{3}y[/tex] ----> equation C

we know that

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

so

[tex]0.021x+0.025y+0.015z=231.69[/tex] ----> equation D

substitute equation B and equation C in equation D

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

solve for y

[tex]221.34-0.0315y+0.025y+0.005y=231.69[/tex]

[tex]0.0015y=231.69-221.34[/tex]

[tex]0.0015y=10.35[/tex]

[tex]y=\$6,900[/tex]

Find the value of x

[tex]x=10,540-\frac{4}{3}(6,900)[/tex]

[tex]x=\$1,340[/tex]

Find the value of z

[tex]z=\frac{1}{3}(6,900)[/tex]

[tex]z=\$2,300[/tex]