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 satisfies the given requirements, we can break down the problem and calculate the exact amounts the investor should allocate to each investment option.

Let's denote the amounts invested in the first, second, and third options as X, Y, and Z, respectively. We know that X + Y + Z = $500,000 (total investment amount).

The goal is to achieve an average return of 15%. We can calculate the weighted average return using the formula:

(X * 15% + Y * 10% + Z * 18%) / (X + Y + Z) = 15%

Simplifying this equation, we get:

0.15X + 0.1Y + 0.18Z = 0.15(X + Y + Z)
0.15X + 0.1Y + 0.18Z = 0.15 * $500,000

Next, the investor wants the amount in the third alternative (Z) to be 40% of the total investment. Mathematically, this can be expressed as:

Z = 0.4 * (X + Y + Z)

Now, we have two equations with two variables (X and Y) that we can solve to find the specific investment amounts:

0.15X + 0.1Y + 0.18Z = 0.15 * $500,000
Z = 0.4 * (X + Y + Z)

By substituting the value of Z in the first equation using the second equation, we can solve for X and Y. If a solution exists where X, Y, and Z are positive and X + Y + Z = $500,000, then there is a meaningful investment strategy that satisfies the requirements.

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