Calculating profits for a private fund
One way I heard of, from a friend who ran a similar fund as yours, is to calculate $days of investment and divide the investment as accordingly.  For example, If I invested 10$ for 10 days and you have invested 20$ for 5 days. At the end of the 10th day my $day = 10*10=100, while your $day=20*5=100. If the investement has grown to 100$, the I should get $100/(100+100)*100=$50, you also should get the same. This I guess is equitable, you could try dividing the corpus with above method. It consideres the amount invested as well as the time invested for. I think by the above method, you could also handle the inbetween withdrawals.