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

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

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=(1)/(3)y` ----> equation B

substitute equation B in equation A

`x+y+(1)/(3)y=10,540`

`x+(4)/(3)y=10,540`

`x=10,540-(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-(4)/(3)y)+0.025y+0.015((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-(4)/(3)(6,900)`

`x=\$1,340`

Find the value of z

`z=(1)/(3)(6,900)`

`z=\$2,300`