A rooftop solar hot water heater with collector areas of \(8 \mathrm{~m}^{2}\) and storage of \(640 \mathrm{~L}\) is installed in Phoenix, Arizona, on a house that uses \(160 \mathrm{~L} /\) day of hot water at \(60^{\circ} \mathrm{C}\). Of the total energy required, \(70 \%\) is supplied by solar energy (the solar fraction is \(70 \%\) ) and \(30 \%\) is supplemented with an electric heater. The solar system costs \(\$ 3000\) for installation, whereas an electric water heater and tank for the same supply costs \(\$ 800\) for installation. Assuming that the electricity cost is \(\$ 0.10 / \mathrm{kWh}\) and does not change over time, estimate the simple payback time for the solar hot water heater. The temperature of the water in the main from which it is to be heated is \(10^{\circ} \mathrm{C}\).