I can't see this paying for itself in 5 years if you still have to purchase the solar panels, plus installation charges for everything.
Sorry for the confusion, but I was referring to two different scenarios. When I said 2kW could power a home at night, that was in response to another comment that said it couldn't. I really think that it could, in theory.
My comment about it paying for itself in 5 years was more to my personal situation. I'd charge the battery array at night and use the stored electricity during the day during peak rates. I don't know how much installation would cost, but if I could use 10kWh during the day at off-peak rates instead of peak, I'd probably save $75/mo or $4500 over 5 years, assuming rates stay constant. Figuring $1000 for inverter and installation (not panels, just wiring it into my electrical panel) + $3500 for the battery array.