$4,000 is invested in ABC's stock and $11,000 is invested in her market account
Step-by-step explanation:
Susan purchased company ABC's stock and invested the balance in her money market account
We need to find how much money is invested in stock and how much is invested in her money market account
Assume that she invested $x in ABC's stock and $y in her money market account
∵ She invested $x in ABC's stock
∵ She invested $y in her market account
∵ Her initial investments amount is $15000
∴ x + y = 15000 ⇒ (1)
The interest formula is I = Prt, where P is the initial investment, r is the rate of interest in decimal and t is the time
In ABC's stock:
∵ She invested $x
∴ P = x
∵ The rate is 13%
∴ r = 13% = 13 ÷ 100 = 0.13
∵ t = 1
- Substitute all of these values in the formula of interest above
∴ [tex]I_{ABC}[/tex] = x(0.13)(1)
∴ [tex]I_{ABC}[/tex] = 0.13x
In her market account:
∵ She invested $y
∴ P = y
∵ The rate is 5%
∴ r = 5% = 5 ÷ 100 = 0.05
∵ t = 1
- Substitute all of these values in the formula of interest above
∴ [tex]I_{market}[/tex] = y(0.05)(1)
∴ [tex]I_{market}[/tex] = 0.05y
∵ Her annual income is $1070
- Add the interest of ABC's stock and the interest of her market
account, equate the sum by 1070
∴ 0.13x + 0.05y = 1070 ⇒ (2)
Now we have a system of equations to solve it
Multiply equation (1) by -0.05 to eliminate y
∵ -0.05x - 0.05y = -750 ⇒ (3)
- Add equations (2) and (3)
∴ 0.08x = 320
- Divide both sides by 0.08
∴ x = 4000
- Substitute value of x in equation (1) to find y
∵ 4000 + y = 15000
- Subtract 4000 from both sides
∴ y = 11000
$4,000 is invested in ABC's stock and $11,000 is invested in her market account
Learn more:
You can learn more about the system of equations in brainly.com/question/2115716
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