You are weighing the economic feasibility of installing a geothermal system versus a solar system to supply heat for your building. The following life cycle costs are reported. The study period is $25$ years, and the discount rate is $7\mathrm{.}5\%.$ The total present value of annual energy savings for geothermal heating is $$2,000,000,$ and $$1,500,000$ for solar heating. Which heating system is the most cost$-$effective? Analyze the the Savings$-$to$-$Investment Ratio $($SIR$).$

Geothermal Heating:

Building Size $25000$ sf

Initial Cost $$10/$sf

Annual Operating Cost $$2/$sf

Solar Heating:

Building Size $25000$ sf

Initial Cost $$5$

Annual Operating Costs $$2$