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24 October, 06:55

Consider a homeowner who is replacing his 25-year-old natural gas furnace that has an efficiency of 55%. The homeowner is considering a conventional furnace that has an efficiency of 82% and costs $1600 and a high-efficiency furnace that has an efficiency of 95% and costs $3050. 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 now pays $1200 a year for heating, determine if he should buy the conventional or the high efficiency model. (Round your answer to the nearest integer number of years.)

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  1. 24 October, 07:05
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    10 years

    so it is more then 8 years so less efficient heater is the better buy in this case

    Explanation:

    here the cost of useful heat=0.55*1200=$660/year

    hence,

    the annual cost of heating for 82% heater

    = (cost of useful heat/η)

    =$660/0.82=$805/year

    the annual cost of heating for 95% heater

    =$660/0.95=$695/year

    the annual cost saving for efficient heater

    =$805-$695

    =$110/year

    now extra initial cost=$2700-$1600==>$1100

    so the payback time = extra initial cost/cost saving

    =10 years

    so it is more then 8 years so less efficient heater is the better buy in this case
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