By shopping around, you might be able to get a much higher interest rate on your Money Market or Savings Account. Online banks tend to offer higher rates than traditional banks with a branch network because they don’ the same brand awareness as many traditional banks. They also do not have the expense of operating physical branches.
Discover, Capital One, American express as well as other names you would normally associate with credit cards also operate online banks. Savings and Money Market accounts with these banks have the same FDIC protection as other traditional banks such as Bank of America or Citibank. Because they are online however you may get a much better Savings or Money Market Account interest rate with these banks.