Translation:The first bank was established in nineteen twenty-four.
Why is this sentence not written in the narrative past tense? Of course, I can easily imagine that it could be spoken by someone who actually witnessed the event in this sentence, but is there any other reason? Perhaps events which are known to have occurred with complete certainty do not require the narrative, even if the speaker did not observe them?
Is the narrative past tense the one that ends in -miş? That would only be used in a story. Or some information that you've just learnt from someone else, and you're sharing it with a friend.
The above sentence, however, seems more like what you would read in an encyclopaedia, where it's impossible to see a -miş tense. (You will see -miştir, with the -dir, but never "miş" alone.)
I am really not knowing it. The sentence could be translated : The first bank was established in the year nineteen twenty-four. May be that without yılında somebody would translate the number as "one thousand nine hundred twenty-four" and not as "nineteen twenty-four" as it is usual when speaking about a year in which something happened. But, as I said, I am not really sure of it.
I think if you want to avoid "yılında' you must say "İlk banka bin dokuz yüz yirmi dörDE kuruldu."