I guess if you want to be precise you'll have to calc the ROI for every intermediate period and then put the pieces together.

You start with $100
After 30 days you have $130 and you want to withdraw some $20.
So you stop at this point and have an ROI for the first 30 days of 30%.
Now you start your next period with your new investment sum of $110 (130-20).

In the end you take each ROI times the no. of days you achieved and divide it by the total no. of days of the year.
roi1 *120/365 + roi2 *50/365+..
I guess that should be sufficiently precise.

Heres a more detailed explanation:
How to calculate your return on investment