First of all, finish()
doesn't destroy your process and free up the memory. It just removes the activity from the activity stack. You'd need to kill the process, which is answered in a bunch of questions (since this is being asked several times).
But the proper answer is - Don't do it. the Android OS will automatically free up memory when it needs memory. By not freeing up memory, your app will start up faster if the user gets back to it.
Please see here for a great write-up on the topic.