It might seem like an easy question, why do heat pumps save money but it is a little bit more complex them that. Heat pumps only save money in the long run. The up front cost to install heat pumps is 10-20 thousand dollars depending on your location. This might seem like a lot of money but most people spend thousands a year heating and cooling there house. The savings come from minimal costs to operate the heat pumps. You only need to run a electric pump and compressor. This is by far less then the cost of electric heat, natural gas or other forms. It also doubles as your air conditioning in the summer. These heat pumps are way more effective then normal window air conditioners.
So the simple answer is, over the course of 10-20 years you will hit a break even point as current convential heating/cooling systems and after that point you will have far cheaper bills for heating and cooling.
If the price of traditional energy sources continue to go up, heat pump ROI will be quicker. Along with tax incentives from states and the federal goverment heat pumps are becoming easier to obtain.
Heat pumps are more about saving green house gases in the long run then saving money right now. Most people don’t have 10-20 years worth of heat bills in there avings account to put in one of these systems.