Answer: 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
