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(52898)   (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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