There is a banking System installed within the buffy world. Now your wallet cannot handle all the money you earn on jobs, quests and looted items you sell to pawn shops. At a certain point the ammount of money will slow you down and will make you a perfect target for pickpockets and thieves. Thus the smarted thing is to store your money and precious items at the bank, where it will be safe.

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Your character's money will be stored in his very own bank account and if you ever need to store some items they can be placed in well protected storage containers.