A homeowner wants to replace an electric hot-water heater. There are two models in the store. The inexpensive model costs $280 and has no insulation between the inner and outer walls. Due to natural convection, the space between the inner and outer walls has an effective conductivity three times that of air. The more expensive model costs $310 and has fiberglass insulation in the gap between the walls. Both models are 3.0 m tall and have a cylindrical shape with an inner-wall diameter of 0.60 m and a 5-cm gap. The surrounding air is at 25°C, and the convection heat transfer coefficient on the outside is 15 W/m2 K. The hot water inside the tank results in an inside wall temperature of 60°C. If energy costs 6 ¢/k Wh, estimate how long it will take to pay back the extra investment in the more expensive hot-water heater. State your assumptions.