Why did the composite rate for I bonds issued drop to 6.89% from 9.62% when the Fed has been increasing interest rate? What is the correlation between I bonds rate and Feds fund rate?
I Bond rates are linked to current inflation (which has been falling since June), while the Fed increases interest rates in the hope that inflation decreases more in the future*.
You can look here for the actual data. The bond pays a fixed rate and adjusts for inflation so that your real return is always exactly equal to the fixed rate. That rate is established by the Secretary of the Treasury for the life of the bond without any published rules and not influenced much by the Fed Funds Rate. For example, it stayed at zero from 2020 until November 2022, although the FED increased rates significantly to 3.75% to 4.00%.
This answer explains why the formula
Composite rate = [Fixed rate + (2 x Semiannual inflation rate) + (Fixed rate x Semiannual inflation rate)]
is designed like that.
See TreasuryDirect for details about I bonds.
This answer shows how the semi-annual inflation rate is computed from CPI-U data.
This answer replicates the calculation of the current value on the website of TreasuryDirect.