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A typical combine harvester sells for $500,000. If the value of the combine depreciates 5.41% each
year, how many years will it take to lose half of it's value?
Round your answer to the nearest whole number of years.

Respuesta :

mhanifa

Answer:

  • 13 years

Step-by-step explanation:

  • Initial value = $500000
  • Depreciation rate = 5.41% each year
  • Target value = 1/2*$500000 = $250000
  • Number of years = x

Depreciation can be expressed as function:

  • d(x) = 500000*((100 - 5.41)/100)^x
  • d(x) = 500000*0.9459^x

Having the final value of $250000, we can find x:

  • 250000 = 500000*0.9459^x
  • 0.5 = 0.9459^x
  • log 0.5 = x log 0.9459
  • x =  log 0.5 / log 0.9459
  • x = 12.46 ≈ 13 years rounded

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