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Yes, but your time to double is a fixed period of time hence the maturity date is it not? So if inflation goes to 99% your $50 E bond that you paid $25 for will still not reach maturity (face value) until it's prescribed time, or am I wrong. If i am write that is the key difference.

The I bond if inflation goes to 99% my yield will go up too

If inflation does happen, EE bond rates will go up as well. EE bonds are indexed against the yields of Treasuries on the open market, and the market will move rates in line with inflation. The key difference is that, with I bonds, the tracking against inflation (or, more precisely, CPI) is done by fiat, while with EE bonds, the tracking is driven by market forces. Which is better is open to some debate, and some believe there is worth in diversifying between both inflation-indexed instruments and traditional bonds.
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