If I buy a song off iTunes, the artist gets $.09
Every time I listen to it on Rhapsody, they get $.0022
Some quick division: .09/.0022 = ~41
What this means is that, if I've listened to a song less than 40 times, the artist makes more if I buy it off iTunes. But once I've listened to it 41 times or more, the artist is making more profit if all those listens were on Rhapsody.
Now I don't know about you, but when it comes to songs I like I listen to them a hell of a lot more than 40 times. You say you buy the records you find yourself listening to more often? Then you are taking money out of the artists' pockets, because every 40 listens through the album on Rhapsody is equivalent to buying the album anew on iTunes.
To make it even more lopsided, consider just how many times more you would listen to those songs throughout your lifetime. Buy the CD once, and the artist will never see another cent from you, whereas the streaming services continue to pay them, forever.