It would take an infinite amount of time, no matter how fast you count.
(If you had an infinite amount of time, however, you could count to an infinitely large number, but that would required counting until the end of forever, and forever has no end...)
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599,999 days.
It would take about 3.2 years.
you count one dollar a second so it would probably take you about 31 and a half years.
I recall reading that it would take you 3 weeks to count to a million if you counted all day, taking time off to eat and sleep. So to count to a billion would take 1000 times 3 weeks.
IF you could count continuously - at the rate of one number per seconds (it would take you longer than that to recite them) - it would take more than 11 days.