A tractor-trailer worth $84 000 depreciates 20% the first year and 10% each year thereafter. How much is it worth after 5 years?
value = 84000(.8)(.9)^4
= ....
How do you get the values?
To calculate the value of the tractor-trailer after 5 years, you need to apply the depreciation rate to its original value each year.
First, let's calculate the depreciation for each year:
Year 1: The tractor-trailer depreciates by 20%. This means the value decreases to 80% of the original value.
Depreciation in Year 1 = 20% of $84,000 = $16,800
Value after Year 1 = $84,000 - $16,800 = $67,200
Years 2-5: The tractor-trailer depreciates by 10% each year. This means the value decreases to 90% of the previous year's value.
Now, let's calculate the depreciation for each subsequent year:
Depreciation in Year 2 = 10% of ($67,200) = $6,720
Value after Year 2 = $67,200 - $6,720 = $60,480
Depreciation in Year 3 = 10% of ($60,480) = $6,048
Value after Year 3 = $60,480 - $6,048 = $54,432
Depreciation in Year 4 = 10% of ($54,432) = $5,443.20 (rounded to the nearest cent)
Value after Year 4 = $54,432 - $5,443.20 = $48,988.80 (rounded to the nearest cent)
Depreciation in Year 5 = 10% of ($48,988.80) = $4,898.88 (rounded to the nearest cent)
Value after Year 5 = $48,988.80 - $4,898.88 = $44,089.92 (rounded to the nearest cent)
Therefore, the tractor-trailer is worth approximately $44,089.92 after 5 years.