$1,000 is definitely too ambitious for that much energy. Even just the charging plug for the car is going to take a sizeable bite out of that.

Another way to think about this is that $1,000 is about 20 tanks of gas, assuming you get 400 miles per tank that's 8,000 miles, which is less than a year of driving for the average American. You can increase your budget and still come out way ahead.

The other consideration is that this scheme only works if you only drive at night, otherwise you'll need a battery to store that power while your car is out and about during the day, or you'll need to grid tie and use the grid as your battery.