An investor has $500,000 to spend. Three alternative investments have been identified, earning 15%, 10% and 18%, respectively. A goal has been set to earn average return of 15% on the total investment. In investment alternative 3, the investor invests 30% of the total investment. Determine the amount of money which should be invested in each option to satisfy the requirements of the investor.

To determine the amount of money that should be invested in each option, we can follow these steps:

Step 1: Calculate the total investment amount needed to achieve the average return of 15%.

• Since the investor wants to earn an average return of 15% on the total investment, we can set up the equation: 0.15 * Total Investment = $500,000
• Solving for the Total Investment: Total Investment = $500,000 / 0.15 Total Investment =$3,333,333.33

Step 2: Determine the amount to be invested in option 3.

• The investor plans to invest 30% of the total investment in option 3.
• Calculating the amount to be invested in option 3: Amount to be invested in option 3 = 0.30 * Total Investment Amount to be invested in option 3 = 0.30 * $3,333,333.33 Amount to be invested in option 3 =$1,000,000

Step 3: Calculate the remaining amount available for options 1 and 2.

• Since the investor has $500,000 to spend and has already allocated$1,000,000 to option 3, the remaining amount available for options 1 and 2 can be calculated as: Remaining amount = Total Investment - Amount invested in option 3 Remaining amount = $3,333,333.33 -$1,000,000 Remaining amount = $2,333,333.33

Step 4: Determine the amount to be invested in options 1 and 2.

• The remaining amount will be divided between options 1 and 2.
• Let's assume x represents the amount to be invested in option 1.
• The amount to be invested in option 2 can be calculated as: Amount to be invested in option 2 = Remaining amount - Amount to be invested in option 1 Amount to be invested in option 2 = $2,333,333.33 - x

Step 5: Set up an equation based on the expected average return.

• The average return can be calculated using the weighted average of the returns from each investment option.
• Setting up the equation: (0.15 * x) + (0.10 * (Remaining amount - x)) + (0.18 * $1,000,000) = 0.15 * Total Investment

Step 6: Solve the equation to find the value of x.

• Simplifying the equation: 0.15x + 0.10(Remaining amount - x) + 0.18($1,000,000) = 0.15($3,333,333.33) 0.15x + 0.10(Remaining amount - x) + $180,000 =$500,000 0.15x + 0.10(Remaining amount - x) = $500,000 -$180,000 0.15x + 0.10(Remaining amount - x) = $320,000

• Expanding the equation: 0.15x + 0.10Remaining amount - 0.10x = $320,000 0.05x + 0.10Remaining amount =$320,000

• Rearranging the equation: 0.05x = $320,000 - 0.10Remaining amount 0.05x =$320,000 - 0.10($2,333,333.33 - x) 0.05x =$320,000 - $233,333.33 + 0.10x 0.05x - 0.10x =$320,000 - $233,333.33 -0.05x =$86,666.67 x = $86,666.67 / -0.05 x =$1,733,333.33

Step 7: Calculate the amount to be invested in option 2.

• Using the value of x, we can calculate the amount to be invested in option 2: Amount to be invested in option 2 = Remaining amount - Amount to be invested in option 1 Amount to be invested in option 2 = $2,333,333.33 -$1,733,333.33 Amount to be invested in option 2 = $600,000

Step 8: Finalize the investment amounts.

• The amount to be invested in each option is as follows: Option 1: $1,733,333.33 Option 2:$600,000 Option 3: $1,000,000

Therefore, to satisfy the requirements of the investor and achieve an average return of 15% on the total investment, $1,733,333.33 should be invested in option 1,$600,000 should be invested in option 2, and $1,000,000 should be invested in option 3.