“Ok now what is the battery cost to keep the lights on until midnight?”
No need, most systems today have no batteries - they are grid-tied. If you are not home, or have excess power, it is transferred to the grid and the utility pays you for whatever you generate.
Since peak demand is during the day they come on line just when needed. Soon utilities will not simply be charging customers for power used but when they use it. Likewise if you dump a lot of power into the grid during peak periods you’ll be reimbused at a higher rate than nighttime consumption.
http://www.solarelectricsupply.com/systems/grid-tie/discount-gridtie.html
They are rather expensive but the most expensive piece is not the panels. It is the controls and the inverter. It does pay off after a while but the up front cost is prohibitive - for now.