Question

Manoj, the landscaper buyer intends to buy a new commercial grade lawn mower that costs $\$2800$. He expects it to last about 8 years, and then he can sell it for scrap metal with a salvage value of about $\$240$. Calculate its approximate value after x years (x < 8) assuming that its value depreciates at a constant rate.
$
  A.y = - 320x + 2,560 \\
  B.y = - 240x + 2,800 \\
  C.y = - 320x + 2,800 \\
  D.y = 240x - 2,560 \\
 $

Answer 1

Hint: We will get the constant depreciating value by subtracting the salvage value from the original cost and then dividing the result with 8. So, every year the depreciating value will be deducted from the original value and finally after 8 years it can be sold for its salvage value.

Complete step-by-step answer:
Given that the cost of the lawn mower is $\$2800$ is being bought by Manoj. He expects it to last 8 years and can sell it for $\$240$ which is its salvage value.
We have to find the depreciating value first.
Depreciating value= (Original cost – salvage value)/No. of years it lasts
Original cost=$\$2800$
Salvage value=$\$240$
No. of years=8
Therefore, Depreciating value will be
  $
   = \dfrac{{\left( {2800 - 240} \right)}}{8} \\
   = \dfrac{{2560}}{8} \\
   = \$ 320 \\
 $
So, every year $\$320$ will be depreciated from the original value.
So, after one year the value of the lawn mower becomes
 $
   \to \left( {2800 - 320} \right) \\
   = \$ 2480 \\
 $
After two years, the value of the lawn mower becomes
  $
   \to 2800 - \left( {2 \times 320} \right) \\
   = 2800 - 640 \\
   = \$ 2160 \\
 $
After ‘x’ (x < 8) years, the value of the lawn mower, say ‘y’, becomes
  $
   \to 2800 - \left( {x \times 320} \right) \\
  y = 2800 - 320x \\
  y = - 320x + 2800 \\
 $
Therefore, from among the options given in the question option C is correct which is $y = - 320x + 2800$
So, the correct answer is “Option C”.

Note: Depreciating value is used to decrease the carrying value over time. Salvage value is the final or remaining value after all depreciation has been done.