Vary invested for equal return quantity

Question

I have $300,000 to disburse among 8 different stocks. The interest earned are 343%, 36%, 35%, 32%, 9%, 9%, 6% and 3%. The amount invested in each needs to be determined, which will vary in quantity, in order to achieve an equal return (ie. the $ return earned from position 1 is the same as 2-8). The return also needs to be determined.

Please, provide equation and answer. I don't math this well anymore.

Thank you.

Answer 1

I have $300,000 to disburse among 8 different stocks. The interest earned are 343%, 36%, 35%, 32%, 9%, 9%, 6% and 3%.

We know that there will be 8 returns of equal value (I will use y here for one of the original investment amounts to show the math) so:

3.43y = x

y = x/3.43 (the original investment is equal to our return divided by 3.43)

Now that we know how to represent each investment in terms of x (the return of each investment) we can set the sum of the investments equal to 300,000:

x/3.43 + x/0.36 +.... = 300,000

Now we can factor out x:

(x)(1/3.43 + 1/0.36 + 1/0.35+.... 1/0.03) = 300,000

(x)(81.273688) = 300,000

x = 3691.231532 or about $3691.23

Remember this is our return, we can't multiply this by 8 to check our answer (like I just tried lol).

To determine how much is invested in each, we have to take x and divide it by 3.43 (for the first) and 0.36 for the second... and so on.

I spent a lot of time on this already, so I'm not going to check for mistakes. Double check the numbers and calculations to make sure there aren't any obvious mistakes. That was one of the toughest algebra questions I've seen.

Hope this helps!