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Homework Help: Energy efficiency - purchasing the right furnace

  1. Jan 29, 2012 #1

    JJBladester

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    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. jcsd
  3. Jan 29, 2012 #2

    Redbelly98

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    Looks good to me. :smile:
     
  4. Jan 30, 2012 #3

    JJBladester

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    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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