1. The problem statement, all variables and given/known data Consider a homeowner who is replacing his 25-year-old natural gas furnace that has an efficiency of 55 percent. The homeowner is considering a conventional furnace that has an efficiency of 82 percent and costs $1600 and a high-efficiency furnace that has an efficiency of 95 percent and costs $2700. The homeowner would like to buy the high-efficiency furnace if the savings from the natural gas pay for the additional cost in less than 8 years. If the homeowner presently pays $1200 a year for heating, determine if he should buy the conventional or high-efficiency model. 2. Relevant equations None. I just want to know if what I'm doing below is mathematically sound. The answer I got seems reasonable but I'd like somebody else to look through my calculations. 3. The attempt at a solution Cost per year of conventional furnace = $1,200*(.55/.82) = $805 Cost per year of high-efficiency furnace = $1,200*(.55/.95) = $695 Savings per year with conventional furnace = $1,200 - $805 = $395 Savings per year with high-efficiency furnace = $1,200 - $695 = 505 Difference in savings (high eff. vs. conventional furn.) = $505 - $395 = $110 $110 * 8 = $880 Additional initial cost of high-efficiency furnace = $2,700 - $1,600 = $1,100 The additional initial cost of the high-efficiency furnace exceeds the savings difference over 8 years. Therefore, the homeowner should buy the conventional furnace.