Answer:
4.1 years.
Step-by-step explanation:
We have been given that The Lisbon’s new heat pump cost $4,500. They bought it to replace their old furnace and air conditioner which cost about $2,800 a year to run. The heat pump will save them approximately 39% a year.
Yearly cost was 2800 at first and the pump will save 39% of 2800. So annual saving with new heat pump will be:
[tex]\frac{39}{100}*2800=0.39*2800[/tex]
Let x be the number of years in which heat pump will pay for itself, so saving in x years will be:
[tex]0.39*2800*x[/tex]
Now let us equate the savings by new heat pump with cost of heat pump to find the number of years (x).
[tex]0.39*2800*x=4500[/tex]
[tex]1092*x=4500[/tex]
[tex]x=\frac{4500}{1092}[/tex]
[tex]x=4.1208791208791209\approx 4.1[/tex]
Therefore, the heat pump will pay for itself in 4.1 years.
