Question

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.)

Answer 1

10 years

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

Step-by-step 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