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 is $3640

the amount invested in the stock portfolio is $5175

the amount invested in the savings account is $1725

Step-by-step explanation:

Let x be the amount invested in CDs.

Let y be the amount invested in the stock portfolio.

Let z be the amount invested in the savings account.

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. It means that

x + y + z = 10540- - - - - - - - - - - - 1

The interest earned from the amount invested in certificates of deposit (CDs) after 1 year is

0.021 × x = 0.021x

The interest earned from the amount invested in stock portfolio after 1 year is

0.025 × x = 0.025y

The interest earned from the amount invested in the savings account after 1 year is

0.015 × x = 0.015z

She would like to make $231.69 in annual interest from her investments. It means that

0.021x + 0.025y + 0.015z = 231.69- - - - - - -2

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. It means that

z = y/3

Substituting z = y/3 into equation 1 and equation 2, it becomes

x + y + y/3 = 10540

Multiplying both sides of the equation by 3, it becomes

3x + 3y + y = 31620

3x + 4y = 31620- - - - - - - - - -3

0.021x + 0.025y + 0.015 × y/3 = 231.69

Multiplying both sides of the equation by 3, it becomes

0.063x + 0.075y + 0.015y = 695.07

0.063x + 0.09y = 695.07- -- - - - - -4

Multiplying equation 3 by 0.063 and equation 4 by 3, it becomes

0.189x + 0.252y = 1992.06

0.189x + 0.27y = 2085.21

Subtracting, it becomes

- 0.018y = - 93.15

y = - 93.15/-0.018

y = 5175

z = y/3 = 5175/3

z = 1725

Substituting y = 5175 and z = 1725 into equation 1, it becomes

x + 5175 + 1725 = 10540

x + 6900 = 10540

x = 10540 - 6900

x = 3640