Interest - paid monthly or annually?

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A very basic question - are there any pros and cons when choosing between interest paid monthly or annually on a saving account?
If paid monthly, does this mean it is compounded? (Surely not then of course everyone will choose this option?)
If paid monthly, does this mean it is compounded? (Surely not then of course everyone will choose this option?)
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If the AER is the same for annual vs monthly, then I tend to choose monthly (paid into the same account) so that interest is spread evenly over different tax years. It's also nice to watch your savings grow !
Some people choose monthly interest and have it paid away because they want it as a source of regular income.
I selected annual for my savings… but wondered if I missed something eg if paid monthly into account:
month 1: interest on deposit
month 2: interest on (deposit + interest the month before)
Where else the interest wouldn’t compound if paid annually eg %interest on initial deposit only.
sorry, a bit thick! 😅😅
It's entirely possible I may have remembered incorrectly, though
Also, although they are clearly two different, independent products in this instance, NS&I always pay a slightly lower rate of interest in AER terms on the monthly interest, paid out of the account, Guaranteed Income Bond in comparison to the yearly interest, paid into the account, Guaranteed Growth Bond. Thus if a 3 year Guaranteed Growth Bond is paying 2.35% gross AER for example, the concurrent 3 year Guaranteed Income Bond will probably be paying 2.30% gross monthly, 2.32% AER.
There are probably a few other savings providers who do similar to the above but on the same account rather than two distinct accounts, and thus they reward a little less those opting for monthly rather than annual interest.