Exactly, so say you are running it 3 hours a day every day and it costs x an hour and you want an ROI on your hardware of 3 months. If y is the cost of building it...
if 3x * 90 > y
build
else
rent
So at $13.338 (assuming no reserved instance) if y is less than $3600 you make your money back in 3 months. Of course a machine with those stats will not be $3600.
Your math is off. At $13.338/hour you're looking at just shy of 10 grand per month ($9763 for a month of 30.5 days.)
It looks like one of these bad boys would set you back about $40000. So you'd break even at 4 months. If you're going to go for the 3 year reserved instance, with $100K upfront, you'd be way better off on capex and opex just buying and colocating the thing (not considering other expenses.)
The bigger you grow the more the balance tips towards do it yourself because your costs for colocation, managing hardware, etc amortize out better with scale. AWS gets a little better with scale but not nearly as quickly.
My math isn't off... it's for 3 hours a day and I state that in my post (perhaps not clearly enough). Your number is for 24. The point was if you're not full utilization it could make sense.
if 3x * 90 > y build else rent
So at $13.338 (assuming no reserved instance) if y is less than $3600 you make your money back in 3 months. Of course a machine with those stats will not be $3600.