SOLUTION: A person plans to invest a total of $80,000 in a money market account, a bond fund, an international stock​ fund, and a domestic stock fund. She wants 60% of her investment to b

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Question 1157223: A person plans to invest a total of $80,000 in a money market account, a bond fund, an international stock​ fund, and a domestic stock fund. She wants 60% of her investment to be conservative (money market and bonds). She wants the amount in domestic stocks to be 4 times the amount in international stocks. Finally, she needs an annual return of $3,200. Assuming she gets annual returns of 2.5% on the money market account, 3.5% on the bond fund, 4% on the international stock fund, and 6% on the domestic stock fund, how much should she put in each investment?
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.

According to the condition, 60% of $80000, i.e. 0.6*80000 = 48000 dollars go to 
the money market and a bond account.

The rest, $80000 - $48000 = $32000 go the the international stock fund and domestic stock fund.


Let x be the amount to invest to the international stock fund; then the amount going
to the domestic stock fund is 4x dollars, according to the condition.

So, our first equation is

    x + 4x = 32000

giving  

    5x = 32000,

     x = 32000/5 = 6400.


Thus $6400 go to the international stock fund and 4*6400 = 25600 dollars go to the domestic stock fund.


These two investments produce  the annual interest of 0.04*6400 + 0.066*25600 = 1792 dollars.


Hence, we should get the rest  annual return of 3200-1792 = 1408 from two other funds, the money market account and the bond fund.


Let y be the amount to invest to bond fund.

Then the amount to invest to the money market account is  48000-y.


We then have this equation

    0.035y + 0.025(48000-y) = 1408.


From the equation,

    y =  = 20800.


Thus $20800 goes to the bond fund, and the rest 48000-20800 = 27200 dollars go to the market account.


ANSWER.  $27200 to the narket account;  $20800 to the bond fund;  $25600 to the domestic stock and $6400 to the international stock fund.

Solved.



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