Geothermal energy is a renewable, sustainable energy resource. Geothermal systems are available for a wide variety of applications.

Mr$.$ Naz Metz must replace his current system and is considering several options to make it more energy efficient. His current energy

bill for heating and cooling is approximately $$5,500$ per year. Replacing his current system with a traditional heating and air

conditioning split system $($HVAC system$)$ costs about $$9,000.$ This replacement system would reduce his annual energy bill by

approximately $20\%$ due to increased efficiency of the condenser. As an alternative, Mr$.$ Metz could install a residential geothermal

system. This system would cost approximately $$20,500$ but promises to reduce his annual energy cost to $45\%$ of its current level. The

life expectancy of either system is $10$ years with neither system having a salvage value at that time. Mr$.$ Metz's personal MARR is $5\mathrm{.}5\%$

per year. The annual worth of the HVAC system is $$-94\mathrm{.}03$ and the annual worth of the geothermal system is $$305\mathrm{.}27.$ At what value of MARR would the systems b e considered equivalent based on annual worth comparison? Hint provided: P is the amount of initial costs for an alternative, A is the energy savings for an alternative.

i is the MARR. Note that i needs to be a decimal if using mathematical formula, i $=0\mathrm{.}055$ for $5\mathrm{.}5\%.$

n is the life expectancy of either system, n $=10.$

Find the value of i that equates the annual worths of the two alternatives. This problem can be solved by using factor tables

provided in Appendix A$,$ by using Excel functions, or by using the formula approach in conjunction with the Goal Seek

functionality.