This setting is quite buried as Apple doesn’t want you to know that you can pay less than what you’re actually paying. We tried different scenarios, and it was quite hard to find the new annual plan — but it’s real.
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.