A homeowner is thinking about buying an electric heat pump to save on heating costs. The heat pump is said to reduce fuel consumption by 10 MMBtu per year for 20 years. It costs $1,400 upfront and uses 100 kwh of electricity annually. The homeowner can get financing at an 8% annual rate, and electricity costs are expected to stay at 24 cents per kwh. Natural gas costs are expected to stay at $15 per MMBtu. To maintain clarity and organization, it is advised to list these assumptions in a spreadsheet table.

Assuming that natural gas is unavailable, the homeowner has resorted to heating the home using fuel oil instead. The price of fuel oil is $25 per MMBtu, which is slightly over $3 per gallon. The expenses for the heat pump and its electricity consumption remain unchanged.

With a $50 per metric ton carbon tax in place, does it make financial sense to invest in a heat pump, considering the potential savings from avoiding carbon taxes:

a) If using natural gas to heat the home?

b) If using fuel oil to heat the home?