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)

Well, let's do some math and see if there's a meaningful investment strategy that satisfies these requirements!

First, let's figure out how much the investor wants to invest in the high-return investment alternative. They want it to be 40 percent of the total investment, which would be 40 percent of $500,000. So, they want to invest $200,000 in this alternative.

Now, let's calculate the expected return from this investment. The interest rate is 18 percent, so the expected return would be 18 percent of $200,000, which is $36,000.

To achieve an average return of 15 percent in the three investments, the total return from all three investments needs to be $75,000. Let's call the total investment in the other two alternatives X.

The first alternative has an interest rate of 15 percent, so the return from this investment would be 15 percent of X.

The second alternative has an interest rate of 10 percent, so the return from this investment would be 10 percent of X.

So, the equation we have is:

$36,000 + 15% of X + 10% of X = $75,000

To make it a bit easier, let's convert percentages to decimals:

$36,000 + 0.15X + 0.10X = $75,000

Combining like terms:

0.25X = $75,000 - $36,000

0.25X = $39,000

Dividing both sides by 0.25, we get:

X = $156,000

So, the total investment in the other two alternatives needs to be $156,000.

Now, let's sum up the amounts invested in each alternative:

Amount in the high-return investment alternative: $200,000
Amount in the other two alternatives: $156,000

If we add these amounts, we get:

$200,000 + $156,000 = $356,000

Uh-oh! We have a problem here. The total amount invested is only $356,000, which is less than the original amount the investor had to spend, $500,000.

So, unfortunately, there is no meaningful investment strategy that satisfies these requirements. It seems like the investor will need to adjust their expectations or look for alternative investment options.

Remember, investing can be a tricky business, but don't be too clownish with your money!

To determine whether there is a meaningful investment strategy that will satisfy the given requirements, we can follow these steps:

Step 1: Calculate the amount the investor wants to invest in the high return investment alternative:
- The investor wants the amount in this alternative to equal 40 percent of the total investment.
- So, the amount to be invested in the high return investment alternative is: 0.40 * $500,000 = $200,000.

Step 2: Calculate the remaining amount available for the other two investments:
- The total investment amount is $500,000, and $200,000 of that will be invested in the high return investment alternative.
- So, the remaining amount available for the other two investments is: $500,000 - $200,000 = $300,000.

Step 3: Determine whether it is possible to achieve an average return of 15 percent with the remaining amount:
- The investor wants an average return of 15 percent in the three investments.
- Let's assume the remaining amount ($300,000) is split equally between the other two investments.
- Let x be the annual interest rate of each of these investments.
- The average return can be calculated as: (15% + x + x) / 3 = 15%.
- Simplifying the equation, we get: (30% + 2x) / 3 = 15%.
- Multiplying both sides by 3, we get: 30% + 2x = 45%.
- Subtracting 30% from both sides, we get: 2x = 15%.
- Dividing both sides by 2, we get: x = 7.5%.

Step 4: Check if the calculated interest rate (7.5%) is achievable:
- The third investment has an expected annual interest rate of 18%.
- Since the goal is to have an average return of 15%, the interest rate of the remaining two investments cannot be higher than 15%.
- Therefore, an interest rate of 7.5% is achievable.

Conclusion:
Based on the calculations, it is possible to have a meaningful investment strategy that satisfies the given requirements. The investor can invest $200,000 (40% of the total investment) in the high return investment alternative and split the remaining $300,000 equally between the other two investments, aiming for an interest rate of 7.5% for each of them. This strategy would result in an average return of 15% for the three investments.