Need method for equitable distribution of profits

[Zengi]

Hello Ladies and Gentlemen.

Im in need of a mathamatical formula that will help me solve difficult mathematical problems.

Its for a project im running and believe me this one is a tough one, my brain is pushing it to the limits.

Its like a riddle, here are the details..

A little Background information:

I am running a trading programme for my clients, they all invest different amounts of money in to one account which i manage and generate profits everyweek.

At the end of the week i split the profits amongst the clients and pay them individually.

Now heres the tricky part...

I keep 50% of the profits and share the remaining 50% amaingst the numerous clients.

The issue now is that one client deposited 250$ whislt another one deposited 400$ with me plus a third one deposited 300$

Lets say i made a profit off 800$ in trading that week.

As stated i get 50% so 400$ is mine as commision and 400$ gets shared amongst the clients. but how do i share this equally amongst the clients.

Before you calculate that id like to point out that there is also another inportant factor that needs adding.

The clients only get paid the profits and not their initial deposit they made at the beginning and on top of that 25% of the profits designated to each individual gets added to their account on top of the innitial deposit they had made allowing them to grow their opportunity to gain more profits in the future.

So okay easier said then done, alright i had at one point 3 clients, i was able to manage with the maths but having said that i now have 23 clients and my mind just cant take it anymore with the growing deposits and individuals and what percentage who should get or added to theire account.

Im looking for a formula i can use on a weekly basis with each new profits set for that week and new participants, who ever can help me i will invite them personally to join my trading society/group if its in your intrest, free of charge, where you can learn to trade or start trading with me, or a amazon gift voucher if its not your thing.

I might want to change my commission % rate lowering it.
Also the number or participants vary each week as they can withdraw up to all of the funds which are in their name.

Just need a formula so i can treat everyone fairly, thats all really.

Thank you all.

@anonymousmoneymaker (IG account)

 

[MarkFL]

Hello, and welcome to FMH!

I've moved your thread since this doesn't involve calculus, edited your post to remove your email addy (never a good idea to post that publicly), and given your thread a descriptive title.

 

[JeffM]

This is simply what stock organizations do every day, particularly mutual funds.

Let's first ignore the issue that different people invest at different times. Let's first deal with different people investing different amounts at the same time.

Suppose the amount collectively invested is x at the beginning of the period, the aggregate profits are y during the period, z is the remaining amount invested collectively at the end of the period, and w is the amount paid to the investors at the end of the period.

[MATH]w = 0.75 * 0.5 * y = 0.375y \text { and } z = x + 0.25 * 0.5 y = z = x + 0.125y.[/MATH]
Investor A gets paid

[MATH]a * w, \text { where } a = \dfrac{\text {Investor A's investment at the beginning of the period}}{x}[/MATH]
Investor B's investment at the end of the period is

[MATH]b * z, \text { where } b = \dfrac{\text {Investor B's investor B's investment at the beginning of the period}}{x}[/MATH]
In other words, you compute payout and the ending value of the investments in the aggregate, which should be very simple. Then you calculate the payouts and ending value in proportion to each investor's proportion of the initial investment.

Now there are practical complications, such as what happens with losses and how to deal with fractional payments. I cannot respond to those because you have not told us what the contractual terms are.

 

[HallsofIvy]

In your particular example, there was a total of 250+ 400+ 300= 950$ invested.

Client A, who invested 250$ invested \(\displaystyle \frac{250}{950}= \frac{5}{19}\) of that so should receive $\frac{5}{19}$ of the 400$ profit or \(\displaystyle \frac{5}{19}(400)= $105.26\).

Client B who invested 400$ invested \(\displaystyle \frac{400}{950}= \frac{8}{19}\) of that so should receive \(\displaystyle \frac{8}{19}\) of the 400$ profit or \(\displaystyle \frac{8}{19}(400)= $168.42\).

Client C who invested 300$ inveted \(\displaystyle \frac{300}{950}= \frac{6}{19}\) of that so should receive \(\displaystyle \frac{6}{19}\) of the 400$ profit or \(\displaystyle \frac{6}{19}(400)= $126.32\).

Of course 105.26+ 168.42+ 126.32= 400.

(I think keeping 50% of the profits for yourself when you have not invested any money is outrageous. Have you cleared this with the Securities Exchange Commission?)

 

[Zengi]

Yes