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 \( \$ \square \) in the money market account. (Type a whole number.)

Let’s break down the investment scenario into manageable parts for clarity! Let: - \( M \) = amount in the money market account - \( B \) = amount in the bond fund - \( I \) = amount in the international stock fund - \( D \) = amount in the domestic stock fund From the problem, we know: 1. The total investment is \( M + B + I + D = 110,000 \) 2. The conservative investments (money market and bonds) make up \( 60\% \) of the total: \[ M + B = 0.6 \times 110,000 = 66,000 \] 3. The international stocks are one-fourth the amount in domestic stocks: \[ I = \frac{1}{4}D \] Next, let's express everything in terms of \( D \): 1. From equation 2: \( M + B = 66,000 \) 2. Now express \( I \) in terms of \( D \): \( I = \frac{1}{4} D\) 3. Substitute \( I \) into the total investment equation: \[ M + B + \frac{1}{4}D + D = 110,000 \] Which simplifies to: \[ M + B + \frac{5}{4}D = 110,000 \] Now, we have two equations: 1. \( M + B = 66,000\) 2. Replacing \( M + B \) with \( 66,000 \) in total: \[ 66,000 + \frac{5}{4} D = 110,000 \] Subtract \( 66,000 \): \[ \frac{5}{4}D = 44,000 \] Multiply both sides by \( \frac{4}{5} \): \[ D = \frac{4}{5} \times 44,000 = 35,200 \] So, \( D = 35,200 \). Now find \( I \): \[ I = \frac{1}{4} D = \frac{1}{4} \times 35,200 = 8,800 \] Now substitute \( D \) back into the first equation for \( M + B \): \[ M + B = 66,000, \] Now we need to calculate the returns for equation: \[ 0.025M + 0.035B + 0.04I + 0.06D = 4,400 \] Substituting \( I \) and \( D \): \[ 0.025M + 0.035B + 0.04(8,800) + 0.06(35,200) = 4,400 \] Calculating these: \[ 0.025M + 0.035B + 352 + 2,112 = 4,400 \] Thus, \[ 0.025M + 0.035B = 4,400 - 2,464 = 1,936 \] Now we have two equations: 1. \( M + B = 66,000 \) 2. \( 0.025M + 0.035B = 1,936 \) Multiply the second equation by 1,000 to eliminate decimals: \[ 25M + 35B = 1,936,000 \] Now we can express \( B \) from \( M + B = 66,000 \): \[ B = 66,000 - M \] Substituting for \( B \) we get: \[ 25M + 35(66,000 - M) = 1,936,000 \] \[ 25M + 2,310,000 - 35M = 1,936,000 \] Combining like terms: \[ -10M + 2,310,000 = 1,936,000 \] Subtract \( 2,310,000 \): \[ -10M = -374,000 \] Dividing by -10: \[ M = 37,400 \] Thus, we have: \[ M = 37,400 \] So, the investor should put \( \$ 37,400 \) in the money market account.