Is there a way to pay annually?
Is there an annual subscription fee for icloud storage?
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There is no annual payment option for iCloud Storage, only monthly. There are two methods by which you can add credit to your Apple ID sufficient to cover a year's subscription: you could buy sufficient ' iTunes and App Store' (not Apple Store) gift cards and redeem them in your account in iTunes/Apple Music, or you could use your registered payment method to add credit to your account - please see Add money to your Apple ID balance - Apple Support
Note that in both cases this credit will also be used for any music,movie or app purchases so you would have to take that into account.