A Carnot heat pump provides $200000$ k$($J$)/($h$)$ to a house to maintain it at $25\backslash$deg C$.$ Throughout the month of December $(31$ days$),$ the heat pump operates $4$ hours per day to transfer heat from a heat source to the inside of the house. There are two options for the outside energy source: Option $1$ is to use the outside air at $0\backslash$deg C as the energy source and Option $2$ is to use lake water at $10\backslash$deg C as the energy source. If electricity costs $0\mathrm{.}1($kW$)/($h$)$ determine how much money can be saved in December by using the lake water as opposed to the air. Note: $1($kW$)/($h$)$

$=1$kJ $.($ h$)/($s$).$