An investor plans to put a total of \( \$ 110,000 \) 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). The investor wants the amount in international stocks to be one-fourth the amount in domestic stocks. Finally, the investor needs an annual return of \( \$ 4,400 \). Assuming the investor 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 the investor put in each investment? The investor should put \( \$ 8800 \) in the international stock fund. (Type a whole number.) The investor should put \( \$ \square \) in domestic stock fund. (Type a whole number.)

To solve this problem, we first define the amounts the investor puts into each fund: Let \( x \) be the amount in the domestic stock fund. Since the investor puts \( \$ 8,800 \) in the international stock fund, the relation between the international stock fund and the domestic stock fund is: \[ \text{International Stocks} = \frac{1}{4} \times \text{Domestic Stocks} \] This means: \[ \$ 8,800 = \frac{1}{4} x \implies x = 4 \times 8,800 = \$ 35,200 \] Next, we denote the investments in the money market account and the bond fund. Since \( 60\% \) of her total investments are conservative (money market + bond fund), we have: \[ 0.6 \times 110,000 = \$ 66,000 \] The total investment must add up to \( \$ 110,000\), so: \[ \text{Money Market} + \text{Bond Fund} + \text{International Stocks} + \text{Domestic Stocks} = 110,000 \] Substituting the known values: \[ \text{Money Market} + \text{Bond Fund} + 8,800 + 35,200 = 110,000 \] This simplifies to: \[ \text{Money Market} + \text{Bond Fund} = 110,000 - 44,000 = 66,000 \] Next, we need to ensure that the investor gets an annual return of \( \$ 4,400 \). The returns from each of the investments can be expressed as: \[ 0.025 \times \text{Money Market} + 0.035 \times \text{Bond Fund} + 0.04 \times 8,800 + 0.06 \times x = 4,400 \] Substituting for \( x \): \[ 0.025 \times \text{Money Market} + 0.035 \times \text{Bond Fund} + 0.04 \times 8,800 + 0.06 \times 35,200 = 4,400 \] Calculating the returns from international and domestic stocks: \[ 0.04 \times 8,800 = 352 \] \[ 0.06 \times 35,200 = 2,112 \] Now the expression for total return is: \[ 0.025 \times \text{Money Market} + 0.035 \times \text{Bond Fund} + 352 + 2112 = 4,400 \] This simplifies to: \[ 0.025 \times \text{Money Market} + 0.035 \times \text{Bond Fund} = 4,400 - 2,464 = 1,936 \] Now we have two equations to solve: 1. \(\text{Money Market} + \text{Bond Fund} = 66,000\) 2. \(0.025 \times \text{Money Market} + 0.035 \times \text{Bond Fund} = 1,936\) We can express the Bond Fund in terms of the Money Market (let's denote it as \( y \)): \[ y = 66,000 - \text{Money Market} \] Now substitute this in the second equation: \[ 0.025 \times \text{Money Market} + 0.035 \times (66,000 - \text{Money Market}) = 1,936 \] Now, solving this equation will give the exact amounts each investment should get. Finally, solving for how much the investor puts in the domestic stock fund yields: The investor should put \( \$ 35,200 \) in the domestic stock fund.