Did Zimbabwe have an inflation of 89.7 sextillion percent?
The figures you question are from Hanke and Kwok (2009).


According to Hanke and Kwok (2009), yes.
A stock (Old Mutual) was listed on both the London Stock Exchange (in GBP) and the Zimbabwe Stock Exchange (in Zimbabwe dollars). Under the assumptions of price arbitrage and purchasing power parity, one can infer Zimbabwe's inflation rate.
I haven't carefully attempted to replicate their work, but I can see no reason to question Hanke and Kwok's general methodology.
The Economist's figure of 500 billion percent is for Sep 2008. (Hanke and Kwok's estimate for Sep 2008 is 471 billion percent.) The higher figure of 89.7 sextillion percent is Hanke and Kwok's estimate for the month to Nov 14, 2008.


Their Table 1: