It really comes down to your individual situation. The money saved with a geo system is a factor of relative fuel costs, system efficiencies, and the amount of heating and/or cooling energy your house consumes in a year. Annual savings can range from next to nothing when compared to a good air-source heat pump in a temperate climate to several thousand dollars a year in high heating or cooling load climates. There are several good web sites that will let you calculate the savings with decent accuracy, I don't have my bookmarks handy but will post when I locate them.

Also, if you let us know your approximate location, current heating/cooling system, and approximate annual operating cost, I or one of the other folks here could give you a quick guesstimate of how much you could save with a GSHP.

Payback can be simple or complicated depending on how you think. Simple payback is just install cost divided by annual savings. A more proper way would be to factor in the cost of capital or opportunity cost (Not sure if these are the right terms, I'm not a money guy), in other words if you invested that $20k, how much would you make on it vs the savings form a heat pump.

New construction or replacement of a failing existing system will also help the payback time. I had a 50 year old boiler that needed to be replaced at a cost of $8500. As my geo system was about $15K, the additional cost was only $6500, so my payback will be a little over 2 years (I think my case is pretty extreme in that regard). If you have a relatively new HVAC system that has years of life left in it, the whole cost of the Geo system must be included, so the payback won't be as good.

If a air to air heat pump was going to cost 10,000 and a geo is estimated at 20,000 then the extra 10,000 is spread out over the savings of using the geo-thermal vs. alternative unit. If geo can save 100 a month over the other unit (yearly average), 1200 a year gives you 8 year pay back. The life expectancy of the geo is most likely 20+ years and the other is ???

This Link provides a useful resource to compare the saving over one method of heating over another.