Question

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. In how many years will the heat

pump pay for itself? Round to the nearest tenth.

Answer 1

4.1 years.

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:

`(39)/(100)*2800=0.39*2800`

Let x be the number of years in which heat pump will pay for itself, so saving in x years will be:

`0.39*2800*x`

Now let us equate the savings by new heat pump with cost of heat pump to find the number of years (x).

`0.39*2800*x=4500`

`1092*x=4500`

`x=(4500)/(1092)`

`x=4.1208791208791209\approx 4.1`

Therefore, the heat pump will pay for itself in 4.1 years.