a person plans to invest a total of $230,000 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 want the amount in domestic stocks to be 4 times the amount in international stocks Finally. she needs an annual return f $9,200. Assuming she gets an annual return of 2.5 % on the money market account and 3.5% on the bond fund,6% on the domestic stock fund, how much should she put in each investment?

Question

a person plans to invest a total of $230,000 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 want the amount in domestic stocks to be 4 times the amount in international stocks Finally. she needs an annual return f $9,200. Assuming she gets an annual return of 2.5 % on the money market account and 3.5% on the bond fund,6% on the domestic stock fund, how much should she put in each investment?

Answer 1

let the amounts (in thousands) in the 4 funds be w,x,y,z respectively. Now the constraints are

w+x+y+z = 230
w+x = 0.6 & 230
z = 4y
0.025w + 0.035x + 0.06y + ?z = 9.2
(you don't give the international % return)
so solve those 4 equations in the usual ways.

Answer 2

Let's break down the problem step-by-step to find the amount she should invest in each account.

Step 1: Calculate the amount needed for conservative investments (money market and bonds).
The person wants 60% of the total investment in conservative money market and bonds.
60% of $230,000 = 0.60 * 230,000 = $138,000

Step 2: Find the amount needed for the domestic stocks and international stocks.
The person wants the amount in domestic stocks to be 4 times the amount in international stocks.
Let's assume the amount in international stocks is x.
Then, the amount in domestic stocks will be 4x.

Step 3: Determine the amount invested in each fund.
To find the amount invested in each fund, we need to consider the total investment and the desired percentages.
Let's assume:
Amount invested in money market account = A
Amount invested in bond fund = B
Amount invested in international stock fund = x
Amount invested in domestic stock fund = 4x

Given that the total investment is $230,000, we can set up the equation:
A + B + x + 4x = 230,000

Step 4: Calculate the annual return for each investment.
The total annual return is $9,200. We can determine the annual return for each investment using the given interest rates.
Annual return on the money market account = 2.5% of A
Annual return on the bond fund = 3.5% of B
Annual return on the international stock fund = 0.06x
Annual return on the domestic stock fund = 0.06(4x)

We can set up the equation:
0.025A + 0.035B + 0.06x + 0.06(4x) = 9,200

Now, we have two equations:
A + B + x + 4x = 230,000 (Equation 1)
0.025A + 0.035B + 0.06x + 0.24x = 9,200 (Equation 2)

We can solve this system of equations to find the values of A, B, and x.

Answer 3

To solve this problem, we can break it down into the following steps:

Step 1: Calculate the total amount for the conservative money market and bonds.
Step 2: Calculate the amount for domestic stocks, given that it should be 4 times the amount for international stocks.
Step 3: Calculate the annual return for each investment.
Step 4: Set up a system of equations to find the amounts to invest in each account.
Step 5: Solve the system of equations to determine the amounts to invest in each account.

Let's start with step 1:

Step 1: Calculate the total amount for the conservative money market and bonds.

The person wants 60% of her investment to be in conservative money market and bonds. So, we can calculate this as:
60% of the total investment = 0.6 * $230,000

Step 2: Calculate the amount for domestic stocks.

The person wants the amount in domestic stocks to be 4 times the amount in international stocks. Let's assume the amount in international stocks is x. So, the amount in domestic stocks would be 4x.

Step 3: Calculate the annual return for each investment.

We know the annual return percentages for each investment type. So, let's compute the annual return for each investment:

Annual return for the money market account = 2.5% of the amount invested in money market account = 0.025 * (0.6 * $230,000)
Annual return for the bond fund = 3.5% of the amount invested in bond fund = 0.035 * (0.6 * $230,000)
Annual return for domestic stock fund = 6% of the amount invested in domestic stock fund = 0.06 * 4x
Annual return for international stock fund = 0 (since we don't know the amount invested yet)

Step 4: Set up a system of equations to find the amounts to invest in each account.

The annual return for all the investments should sum up to $9,200.
So, we can set up the following equation:

(Annual return for the money market account) + (Annual return for the bond fund) + (Annual return for the domestic stock fund) + (Annual return for the international stock fund) = $9,200

Step 5: Solve the system of equations to determine the amounts to invest in each account.

Substituting the calculated annual return values, we get:

(0.025 * (0.6 * $230,000)) + (0.035 * (0.6 * $230,000)) + (0.06 * 4x) + 0 = $9,200

Now, we can solve this equation to find the value of x, which will give us the amount to invest in the international stock fund.

After finding the value of x, we can calculate the amounts invested in the money market account, bond fund, and domestic stock fund using the given percentages and the total investment amount of $230,000.

Note: This explanation provides the steps to solve the problem conceptually. To get the exact amounts, you would need to solve the equation using algebraic techniques.