Is it legal to play music that I paid for, such as CDs, MP3s or digital files for background music?

When you purchase music, whether it be digital files or a CD, you are purchasing a license to “rent” the content for yourself.  No matter how much music you purchase for yourself, that music is prohibited to play in public. Once it’s played in a commercial setting without a proper license, it violates copyright law since it’s then considered a public performance, which requires a separate license.