Question 1196205: A person plans to invest a total of $110,000 in a money market account, a bond fund, an international stock fund, and a domestic stock fundShe 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 $4,400. Assuming she gets annual returns of 2.5% on the money market account, 3.5% on the bond fund4% on the international stock fundand 6% on the domestic stock fund, how much should she put in each investment?
Answer by amoresroy(361)   (Show Source):
You can put this solution on YOUR website! Let X = money that should be invested in money market
Y = money that should be invested in bonds
W = money that should be invested in international stock fund
Z = money that should be invested in domestic stock fund
Equations
(1) X + Y = 0.6(110,000) = 66,000
Y = 66,000 - X
(2) Z = 4W
(3) Z + W = 0.4(110,000)
(4) .025X + .035Y + .04W + .06Z = 4,400
Substitute equation (2) in (3)
4W + W = 44,000
5W = 44,000
W = 8,800
Z = 4(8,800) = 35,200
Express equation (4) in terms of X
.025x + .035(66,000-X) + .04(8,800) + .06(35,200) = 4,400
.025x + 2,310 - .035X = 4,400 - 352 - 2,112
-.01x = 1,936 - 2,310
X = -374/-.01
X = 37,400
Y = 66,000 - 37,400 = 28,600
Answer:
Investment as follows
$37,400 for money market
$28,600 for bonds
$8,800 for international stock fund
$35,200 for domestic stock fund
Solved
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