Database size and cycle
With rare exceptions, do not create identical tables split by year or month or customer or whatever.  If a table is getting slower as it gets bigger, then you don't have the right indexes and/or you need to redesign the queries.  Even a billion rows in a table is not 'unmanageable'.

Clients, bills, banks, transactions -- sounds like about 4 tables, plus some tables for Normalization.  A bill might contain a client_id column, but not the client's name, address, etc.