Although, they can't just lower CD rates. Certificates of Deposit are considered contracts. The rate on your CD is fixed for the term. However, if a bank takes over another bank from an FDIC closure, the new bank can lower the rates, but you also have the right to close your CD without penalty if you don't like the new rates. Another exception is if your bank is considered a savings and loan. Savings and Loans can actually close CDs that are longer than 1-year.