iCloud account
How do I change Payment for iCloud storage
iPhone SE, iOS 12
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There are several ways to change you payment method, including on your computer, or iOS device, or also through the web browser. Attached here is a linked support article: https://support.apple.com/en-us/HT201266
If you want to change your payment type, you still need to go in through the App Store app, as outlined in the support article instructions.
If you cancel your iCloud storage plan (or Apple fails to charge your credit card multiple times), you'll have 30 days to download any data before it's erased from servers. If you just want to switch payment type, you can do this as many times as you need without any penalty. Apple only offers monthly subscriptions, but no annual payment options.