Need help on an investment word problem for precal

Question

a person plans to invest a total of 100,000 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 the domestic stock to be 4 times the amount in the international stocks. Finally, she needs an annual return of $4,000. Assuming she gets an annual return 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 1

First we invent some variables which we hope to reduce as we start to solve the problem. Let m, b, n, d represent the investment amounts for the money market account, the bond fund, the international and domestic stock funds respectively.

Now we can apply the given facts:

m+b+n+d=$100000 (total investment);

m+b=$60000 (60% of $100000);

d=4n, and since n+d=$40000 (40% of $100000), 5n=$40000, n=$8000 and d=$32000.

We also know that after a year the total interest is $4000, so:

0.025m+0.035b+0.04n+0.06d=$4000 (annual return).

We plug in n=8000 and d=32000:

0.025m+0.035b+320+1920=4000;

0.025m+0.035b=4000-2240=1760.

b=60000-m so we substitute for b:

0.025m+0.035(60000-m)=1760.

We can solve this for m:

0.025m+2100-0.035m=1760;

2100-1760=0.01m;

340=0.01m, m=$34000 and b=60000-34000=$26000.

So $34,000, $26,000, $8,000 and $32,000 should be invested in the money market, bond fund, international and domestic stock funds respectively.