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)

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 Crammer Rule)

Well, I must say, this investor seems to have quite the investment juggling act going on! Let's see if we can help them out.

To determine whether there is a meaningful investment strategy, we need to do a little math. Let's call the amount of money invested in the first option "x," the amount in the second option "y," and the amount in the third option "z."

According to the given requirements, the investor wants the average return to be 15 percent, and the amount in the third option to be 40 percent of the total investment. This means that z should equal 0.4 times the total investment, or 0.4 times (x + y + z).

Additionally, we know that the interest rates for the three options are 15, 10, and 18 percent. To achieve an average return of 15 percent, we can set up the following equation:

(0.15x + 0.10y + 0.18z) / (x + y + z) = 0.15

Now, let's substitute z with 0.4 times (x + y + z) in the equation:

(0.15x + 0.10y + 0.18(0.4(x + y + z))) / (x + y + z) = 0.15

Simplifying this equation may require some time and effort, but let's hope it's worth it for our investor friend. By analyzing this equation, we can determine whether there is a meaningful investment strategy that satisfies these requirements.

Remember, investing is a serious business, but sometimes it can feel like juggling rubber chickens while riding a unicycle. Good luck to our investor friend!

To determine whether there is a meaningful investment strategy that will satisfy the given requirements, we need to calculate the amount of money that should be invested in each alternative to achieve an average return of 15 percent.

Let's assume the amount to be invested in the first alternative (with a 15% interest rate) is x.

According to the given information, the amount in this alternative should equal 40% of the total investment. So, we have x = 0.4 * (total investment).

Now, let's calculate the amount invested in the second alternative (with a 10% interest rate). Since the total investment is $500,000 and 40% is already invested in the first alternative, the remaining 60% should be spread between the second and third alternatives. Therefore, the amount invested in the second alternative = 0.6 * (total investment) - x.

Similarly, calculating the amount invested in the third alternative (with an 18% interest rate), we have the amount invested in the third alternative = 0.6 * (total investment) - (amount invested in the second alternative).

To ensure the average return is 15%, we need to calculate the weighted average interest rate:

[(x * 0.15) + ((0.6 * (total investment) - x) * 0.10) + ((0.6 * (total investment) - (amount invested in the second alternative)) * 0.18)] / (total investment) = 0.15

Simplifying the equation, we have:

(0.15x + 0.06 * (total investment) - 0.10x + 0.108 * (total investment) - 0.18 * (amount invested in the second alternative)) / (total investment) = 0.15

0.03x + 0.168 * (total investment) - 0.18 * (amount invested in the second alternative) = 0.15 * (total investment)

Next, we substitute the value of x found earlier:

0.03 * (0.4 * (total investment)) + 0.168 * (total investment) - 0.18 * (amount invested in the second alternative) = 0.15 * (total investment)

0.012 * (total investment) + 0.168 * (total investment) - 0.18 * (amount invested in the second alternative) = 0.15 * (total investment)

Combining like terms:

0.18 * (total investment) - 0.18 * (amount invested in the second alternative) = 0.138 * (total investment)

0.18 * (total investment) = 0.138 * (total investment) + 0.18 * (amount invested in the second alternative)

Now, we can simplify the equation further and find an expression for the amount invested in the second alternative:

0.18 * (total investment) - 0.138 * (total investment) = 0.18 * (amount invested in the second alternative)

0.042 * (total investment) = 0.18 * (amount invested in the second alternative)

Dividing both sides by 0.18, we get:

0.042 * (total investment) / 0.18 = amount invested in the second alternative

0.2333 * (total investment) = amount invested in the second alternative

To analyze whether there is a meaningful investment strategy, we need to determine if this equation provides a feasible solution.

To determine if there is a meaningful investment strategy that satisfies the given requirements, we can follow these steps:

Step 1: Determine the amount to be invested in each alternative.
Let's assume the amount invested in the first alternative (15% interest rate) is x dollars.

According to the given conditions, the amount invested in the second alternative (10% interest rate) will be (40% of the total investment - x) dollars.

Similarly, the amount invested in the third alternative (18% interest rate) will be (60% of the total investment) dollars.

Therefore, the total investment is (x) + (40% of the total investment - x) + (60% of the total investment), which equals to 500,000 dollars.

So, the equation will be:
x + 0.4 * 500,000 - x + 0.6 * 500,000 = 500,000

Step 2: Simplify the equation and solve for x.

Let's simplify the equation:
0.4 * 500,000 - x + 0.6 * 500,000 = 500,000
200,000 - x + 300,000 = 500,000
500,000 - x = 500,000 - 500,000
x = 200,000

Step 3: Evaluate if the investment strategy satisfies the requirements.

Now that we have determined the amount to be invested in the first alternative (15% interest rate), which is $200,000, we can calculate if the average return of the three investments is 15%:

Total return = (Amount invested in 15% alternative * 15%)
+ (Amount invested in 10% alternative * 10%)
+ (Amount invested in 18% alternative * 18%)

Total return = (200,000 * 15%) + (40% of 500,000 - 200,000 * 10%) + (60% of 500,000 * 18%)
= 30,000 + 20,000 + 54,000
= 104,000

Average return = Total return / Total investment
= 104,000 / 500,000
= 20.8%

Since the average return of the three investments is 20.8% instead of the desired 15%, we can conclude that there is no meaningful investment strategy that satisfies all the given requirements.