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.)

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

it was a fall down when it happens

explanation: