$$ 1 \leftarrow \quad \begin{array}{l} ext { An investor plans to put a total of } \$ 110,000 ext { in a money market account, a bond fund, an international } \ ext { stock fund, and a domestic stock fund. She wants } 60 \% ext { of her investment to be conservative (money } \ ext { market and bonds). The investor wants the amount in international stocks to be one-fourth the amount } \ ext { in domestic stocks. Finally, the investor needs an annual return of } \$ 4,400 ext {. Assuming the investor gets } \ ext { annual returns of } 2.5 \% ext { on the money market account, } 3.5 \% ext { on the bond fund, } 4 \% ext { on the international } \ ext { stock fund, and } 6 \% ext { on the domestic stock fund, how much should the investor put in each investment? } \ ext { The investor should put } \$ 37400 ext { in the money market account. } \ ext { (Type a whole number.) } \ ext { The investor should put } \$ \square ext { in the bond fund. } \ ext { (Type a whole number.) }\end{array} $$. $$ \quad $$.

Question

$$ 1 \leftarrow \quad \begin{array}{l}	ext { An investor plans to put a total of } \$ 110,000 	ext { in a money market account, a bond fund, an international } \ 	ext { stock fund, and a domestic stock fund. She wants } 60 \% 	ext { of her investment to be conservative (money } \ 	ext { market and bonds). The investor wants the amount in international stocks to be one-fourth the amount } \ 	ext { in domestic stocks. Finally, the investor needs an annual return of } \$ 4,400 	ext {. Assuming the investor gets } \ 	ext { annual returns of } 2.5 \% 	ext { on the money market account, } 3.5 \% 	ext { on the bond fund, } 4 \% 	ext { on the international } \ 	ext { stock fund, and } 6 \% 	ext { on the domestic stock fund, how much should the investor put in each investment? } \ 	ext { The investor should put } \$ 37400 	ext { in the money market account. } \ 	ext { (Type a whole number.) } \ 	ext { The investor should put } \$ \square 	ext { in the bond fund. } \ 	ext { (Type a whole number.) }\end{array} $$. $$ \quad $$.

UpStudy AI · Accepted Answer

Let x = money market, y = bond fund, a = international stock fund, and b = domestic stock fund. We are given:

1. Total investment:  
  x + y + a + b = 110,000  
  Given x = 37,400.

2. 60% in conservative investments (money market and bonds):  
  x + y = 0.6 × 110,000 = 66,000  
  So, y = 66,000 – 37,400 = 28,600.

3. International stocks equal one-fourth of domestic stocks:  
  a = b/4.

4. Annual returns requirement:  
  0.025x + 0.035y + 0.04a + 0.06b = 4,400.

Substitute x and y into the return equation:  
  0.025(37,400) + 0.035(28,600) + 0.04a + 0.06b = 4,400  
  Compute the conservative returns:  
   0.025 × 37,400 = 935  
   0.035 × 28,600 = 1,001  
  So, conservative returns = 935 + 1,001 = 1,936.  
Subtracting from 4,400 gives the required return from the stock funds:  
  4,400 – 1,936 = 2,464.

Now, from the total investment we know the stocks amount:  
  a + b = 110,000 – 66,000 = 44,000  
Substitute a = b/4:  
  (b/4) + b = 44,000  
  (5b/4) = 44,000  
  b = (44,000 × 4)/5 = 35,200  
  Thus, a = 35,200/4 = 8,800.

Confirm the returns from stocks:  
  International: 0.04 × 8,800 = 352  
  Domestic: 0.06 × 35,200 = 2,112  
  Total: 352 + 2,112 = 2,464, which matches the remaining return needed.

So the investor should put:
  Money market: 37,400  
  Bond fund: 28,600  
  International stock fund: 8,800  
  Domestic stock fund: 35,200

Since the problem asks: "The investor should put $37400 in the money market account. The investor should put $______ in the bond fund."  
The answer for the bond fund is: 28,600.
The investor should put $28,600 in the bond fund.

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