How can I change from monthly to annual billing?

Annual iCloud storage plans - https://support.apple.com/HT201058

"If you're a new iCloud subscriber, you can only choose a monthly iCloud storage plan."

There are now no longer any annual plans, only monthly unless you have a very old plan that is still set to annual payment. If you do not want to add a credit card to your payment information you can use a gift card to make sure your iTunes Store balance has enough money to cover long-term deductions.

You can't, except by using iTunes Store gift cards to prepay the charges.

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