Well-known Barclays bank, however, offers both. The big bank offers an online high-yield savings account that stands out thanks to tools that will help you save, including a personal Barclays ...

CNBC Select looked at what big-name banks offer when it comes to premier checking accounts, and those that stood out are from Bank of America, Chase, Citi, HSBC, Wells Fargo and TD Bank.

As interest rates rose, banks charged more for credit cards and loans, but held rates paid on savings accounts.