A geothermal system is initially more expensive to set up than a conventional he

Question

A geothermal system is initially more expensive to set up than a conventional heating and cooling system but the annual operating cost are much cheaper.

a) How many years would it take for the geothermal system to pay for itself? assume that you need to replace an exiting system and that you can obtain the govt. grant to do so. please show all ur calculations.

-geothermal system cost to install: $20,000                      

 - standard furnace and AC cost to install: $3500
-For a geothermal system, the cost of natural gas to heat the home and operate the hot water tank costs about $150 per month.
-Operating cost for heat pump about $100 per month and without having to pay for electricity for and Air Conditioning would save $400 per year.
Gov't grant: $7500 to encourage people to install

Please solve this and show all calculations

Explanation / Answer

let after x months cost of operating and installing an AC= cost of operating and installign geothermal energy AC= $3500+$100(heat pump)*X+$150(operate hot water)*X-$400/12(400 was for an year so for a month it is 400/12)*X geothermal energy= $20000-$7500(govt grant)+$150*X(for natural gas) so equating AC and geothermal costs for X years we get 3500+650/3 *X=12500+150*X X=135 months =11.25 years i.e; after 11 years 4 months cost of operating of both becomes the same

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