Energy efficiency - purchasing the right furnace

1. Jan 29, 2012

JJBladester

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.

2. Jan 29, 2012

Redbelly98

Staff Emeritus
Looks good to me.

3. Jan 30, 2012

JJBladester

Thanks Redbelly98... One of the harder things in science education is interpreting what word problems are really asking for. The way I interpret a problem may be vastly different than the what the author intended.

-Jeff

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