Question

ana jones asks her broker to divide her 401k investment of $2000 among the international fund, the fixed assets fund, and company stock. she decides that her investment in the international fund should be twice her investment in company stock. during the first quarter, the international fund earns 4.5%, the fixed assets fund earns 2.6%, and the company stock falls 0.2%. at the end of the first quarter, ms jones receives a statement indicating a return of $58 on her investment. how did the broker divide ms. jones initial investment?

Explanation:

Answer:

Let the amount invested in company - stock be $x$. Then the amount invested in the International Fund is $2x$, and the amount invested in the Fixed - Assets Fund is $2000-(x + 2x)=2000 - 3x$.

The return from the International Fund is $0.045\times2x$, the return from the Fixed - Assets Fund is $0.026\times(2000 - 3x)$, and the return from the company stock is $-0.002\times x$.

The total return is $0.045\times2x+0.026\times(2000 - 3x)-0.002\times x = 58$.

First, expand the left - hand side:

$0.09x+52-0.078x - 0.002x=58$

Combine like terms:

$(0.09x-0.078x - 0.002x)+52 = 58$

$0.01x+52 = 58$

Subtract 52 from both sides:

$0.01x=6$

Solve for $x$:

$x = 600$

The amount invested in company stock is $x=\$600$.

The amount invested in the International Fund is $2x = 2\times600=\$1200$.

The amount invested in the Fixed - Assets Fund is $2000-(600 + 1200)=\$200$.

So, $\$1200$ in the International Fund, $\$200$ in the Fixed - Assets Fund, and $\$600$ in company stock.