(adsbygoogle = window.adsbygoogle || []).push({}); 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Energy efficiency - purchasing the right furnace

**Physics Forums | Science Articles, Homework Help, Discussion**