As far as I know, Calvin didn't submit any song to Rihanna for Unapologetic. He said that he didn't have enough time (only two days) to write and produce a track, so he couldn't make it and, as a consequence, he didn't send her a song.
Regarding Rihanna's new album, Calvin mentioned (around the 7:35 min. mark) that he was focused on finishing Motion, so he only sent her a track that was written by Tinashe and him. Being said that, it's not "Dollar Signs" as he said later that he doesn't know what's gonna happen to that song.
I love when someone brings the whole TEA to a story