Banks are thinking about imposing annual fees of $25 or $30 on debit cards, according to people familiar with bank strategies. Other banks will increase fees on checking accounts. For example, during 2011, Bank of America will offer four basic checking accounts in some states, instead of three. Three of the four will offer ways for customers to avoid fees, while the fourth, the Essentials account, has an unavoidable monthly fee between $6 and $9. Chase Bank will charge a $6 monthly fee on one of their checking accounts, however, customers can avoid the fee with a $500 or more monthly deposit to the account, or when they use their debit cards five times during the month.