If you’re not a current Apple Music subscriber, the Music app only lets you subscribe to a normal monthly plan as pictured above. But if you’re an existing subscriber, you can go to your membership settings and switch to an annual plan. So new users will have to buy a monthly subscription first and then switch.
To access the new subscription and save $20/year, open the App Store app, scroll to the bottom of the Featured tab then tap on your Apple ID. Enter your password when prompted and choose 'View Apple ID'. Select the subscriptions button and then locate your Apple Music membership settings.
If you're planning to keep Apple Music for the long term, this option will save you a few dollars.