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?

As she decides that her investment in the International Fund should be twice her investment in company stock, so the investment in International fund will be [tex] 2x [/tex]

If we assume that the investment in Fixed Assets Fund is [tex] y [/tex], then...

[tex] x+2x+y= 2000\\ \\ 3x+y= 2000\\ \\ y= 2000-3x ................................(1) [/tex]

As the International Fund earns 4.5%, so the amount of earning [tex] = 2x*\frac{4.5}{100}= 0.09x [/tex]

Fixed Assets Fund earns 2.6%, so the amount of earning [tex] = y* \frac{2.6}{100}= 0.026y [/tex]

Now the company stock falls 0.2%, so the amount of loss [tex] = x* \frac{0.2}{100}= 0.002x [/tex]

At the end of the first quarter, Ms Jones receives a statement indicating a return of $58 on her investment. So....

[tex] 0.09x+0.026y- 0.002x= 58\\ \\ 0.088x+0.026y=58.................................(2) [/tex]

Now substituting equation (1) which is [tex] y= 2000-3x [/tex] into equation (2), we will get...

[tex] 0.088x+ 0.026(2000-3x)= 58\\ \\ 0.088x+ 52-0.078x= 58\\ \\0.01x +52=58\\ \\ 0.01x= 6 \\ \\ x= \frac{6}{0.01}= 600 [/tex]

Plugging the value of [tex] x=600 [/tex] into equation (1)...

[tex] y= 2000- 3(600)\\ \\ y= 2000-1800\\ \\ y= 200 [/tex]

So, the investment in International Fund, [tex] 2x= 2*600= 1200 [/tex] dollar

Investment in Fixed Assets Fund is [tex] 200 [/tex] dollar and investment in company stock is [tex] 600 [/tex] dollar