How many years of expansion occurred during inflation? During inflation, expansion happens at a very rapid rate. 
How many years of expansion did it fast forward through?
Meaning, if it weren't for inflation, how many years would it take for the universe to expand at its basic rate from the big bang to the size of the universe after inflation?
 A: Inflation is what produces the homogeneous, flat universe that we observe, so if you leave it out, the universe never reaches anything like its present state in any amount of time. If it managed to reach its present size (by whatever metric), it would be far more irregular and probably wouldn't have galaxies, etc.
You could write down a model in which the universe was already homogeneous and flat before inflation, so the universe doesn't "need" inflation to get to its present state. The effect of adding inflation to that model is actually that it takes longer for the universe to reach its present state. The scale factor may increase by a factor of $e^{60}$ or more during inflation, but the scale factor is only meaningful up to an overall rescaling anyway. Physically meaningful quantities like energy density and the Hubble parameter are roughly equal before and after inflation (at least, they change less than during an equivalent period of ordinary expansion), so inflation just "pauses" the expansion for a while. If inflation lasts $10^{-33}\text{ s}$, then it only takes $10^{-33}\text{ s}$ longer to get to the present era, but it does technically take longer.
A: Assuming we have the correct value for the cosmological constant the doubling time, that is the time it will take for the universe to double in size, is around 11.4 billion years.
We have few hard theories about inflation, but suppose the universe expanded by $e^{60}$ as Danu suggests in his comment, then the number of doubling times is $60/ln(2) \approx 87$. The time it will take the current universe to double in size 87 times is about 990 billion years.
You can obviously adapt this sum for whatever number of $e$-foldings your preferred theory of inflation predicts.
Footnote: the doubling time really only applies once the universe has expanded enough to make the density of matter negligable compared to the cosmological constant. However we aren't far off that stage and given how approximate this sum is I don't think it really matters.
