An investor has $ 500000 to spend. There investments are being considered, each having an expected annual interest rate. The interest rates are 15, 10 & 18 percent respectively. The investor`s goal is an average return of 15 percent in the three investments. Because of the high return on investment alternatives, the investor wants the amount in this alternative to equal 40 percent of the total investment. Determine whether there is a meaningful investment strategy which will satisfy these requirements. (BY Grammer Rule)
To determine whether there is a meaningful investment strategy that will satisfy these requirements, we can follow these steps:
Step 1: Calculate the amount of money the investor wants to allocate to the alternative with the higher return. According to the requirements, this amount should equal 40% of the total investment. Since the investor has $500,000 in total, the amount allocated to the high-return alternative would be 40% of $500,000, which is $200,000.
Step 2: Calculate the remaining amount of money after allocating $200,000 to the high-return alternative. To do this, subtract $200,000 from the total investment of $500,000. The remaining amount would be $300,000.
Step 3: Calculate the weighted average return of the remaining two investments. The investor wants an average return of 15%, so the weighted average return of the remaining investments should also be 15%.
Let's assume the amount allocated to the first investment (10% return) is x, and the amount allocated to the second investment (18% return) is y.
Based on the requirement that the weighted average return should be 15%, we can set up the following equation:
(10% of x + 18% of y) / ($300,000) = 15%
Simplifying the equation:
(0.10x + 0.18y) / ($300,000) = 0.15
Step 4: Solve the equation to determine the values of x and y. This will help determine the specific amounts that need to be allocated to the individual investments to achieve the desired weighted average return.
Once you have the values of x and y, verify if they are realistic and feasible investment amounts within the given constraints (e.g., positive and not exceeding the remaining amount of $300,000). If your solution yields feasible values, then there is a meaningful investment strategy that satisfies the given requirements. Otherwise, there might not be a feasible solution.
To determine whether there is a meaningful investment strategy that satisfies these requirements, we need to calculate the amount of money to invest in each alternative.
Let:
- X be the amount invested at 15% interest rate
- Y be the amount invested at 10% interest rate
- Z be the amount invested at 18% interest rate
According to the given conditions:
1) The total investment is $500,000:
X + Y + Z = $500,000 (Equation 1)
2) The average return should be 15%. The sum of the returns for each investment divided by the total investment should equal 15%.
(0.15X + 0.10Y + 0.18Z) / ($500,000) = 15% (Equation 2)
3) The amount invested in the alternative with 18% interest rate (Z) should equal 40% of the total investment.
Z = 0.40 * ($500,000) (Equation 3)
Now, let's solve these equations:
From Equation 2, rewrite it as:
0.15X + 0.10Y + 0.18Z = 0.15 * ($500,000)
Substitute Equation 3 into Equation 2:
0.15X + 0.10Y + 0.18 * 0.40 * ($500,000) = 0.15 * ($500,000)
Simplifying:
0.15X + 0.10Y + 0.072 * ($500,000) = 0.15 * ($500,000)
Now, let's substitute Equation 1 into this equation:
0.15X + 0.10Y + 0.072 * ($500,000) = 0.15 * ($500,000) - X - Y
Simplifying further:
0.15X + X + 0.10Y + Y = 0.15 * ($500,000) - 0.072 * ($500,000)
Combining like terms:
1.15X + 1.10Y = 0.15 * ($500,000) - 0.072 * ($500,000)
Now, let's substitute Equation 1 into this equation:
1.15X + 1.10Y = 0.15 * ($500,000 - X - Y) - 0.072 * ($500,000)
Simplifying:
1.15X + 1.10Y = 0.15 * ($500,000 - X - Y) - 0.072 * ($500,000)
Expanding:
1.15X + 1.10Y = 0.15 * $500,000 - 0.15X - 0.15Y - 0.072 * $500,000
Simplifying further:
1.15X + 1.10Y = 0.15 * $500,000 - 0.15X - 0.15Y - 0.072 * $500,000
Combining like terms:
1.15X + 1.10Y + 0.15X + 0.15Y + 0.072 * $500,000 = 0.15 * $500,000
Simplifying again:
1.15X + 0.15X + 1.10Y + 0.15Y + 0.072 * $500,000 = 0.15 * $500,000
Combining like terms:
1.3X + 1.25Y + 0.072 * $500,000 = 0.15 * $500,000
Simplifying further:
1.3X + 1.25Y + 0.072 * $500,000 = 0.15 * $500,000
Now let's solve this equation to find the values of X and Y.