Out of curiosity, I monitored the electrical usage incurred when I too a quick shower. The total time of the show was about six minutes. As the graph shows at about 9:35 AM the 40 gallon GE electric water heater kicked in. It used an average of 5 kWh of power for a period of six minutes to reheat the water I had used. At ten cents a kilowatt hour, I figured my cost to be less than a penny.
As almost an afterthought, I went down to the basement where the unit is located and covered about three fourths of the tank with insulation that was R rated a value of 4.0. I’m not very confident that doing this will result in much in the way of savings, but I figured it couldn’t hurt.