Question

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.

Answer 1

• 13 years

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