Susan purchased company ABC's stock and invested the balance in her money market account. ABC's stock yielded 13% last year and

Question

2 years ago

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Susan purchased company ABC's stock and invested the balance in her money market account. ABC's stock yielded 13% last year and

her money market account yielded 5% last year. If Susan's initial investments amount to $15000, and the annual income is $1070, how much money is invested in stock and how much is invested in her money market account?

Mathematics

1 answer:

garri49 [273] · Answer 1 · 2022-08-17T22:32:49+03:00

$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

ABC's stock yielded 13% last year and her money market account yielded 5% last year
Susan's initial investments amount to $15000, and the annual income is $1070

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

∴ $I_{ABC}$ = x(0.13)(1)

∴ $I_{ABC}$ = 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

∴ $I_{market}$ = y(0.05)(1)

∴ $I_{market}$ = 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

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