A farmer buys a tractor for $50,000. If the tractor depreciates 10% per year, find the value of the tractor in 7 years. Round to the nearest penny.
To find the value of the tractor in 7 years, we will need to calculate its depreciation each year and subtract it from the original value.
The tractor depreciates by 10% per year. This means that each year, the value of the tractor will decrease by 10% of its previous value.
To calculate the depreciation for each year, we can use the formula:
Depreciation = (Depreciation rate/100) * Previous value
Since the tractor depreciates by 10% per year, the depreciation rate is 10%.
Let's calculate the value of the tractor year by year:
Year 1:
Depreciation = (10/100) * $50,000 = $5,000
Value after Year 1 = $50,000 - $5,000 = $45,000
Year 2:
Depreciation = (10/100) * $45,000 = $4,500
Value after Year 2 = $45,000 - $4,500 = $40,500
Year 3:
Depreciation = (10/100) * $40,500 = $4,050
Value after Year 3 = $40,500 - $4,050 = $36,450
Year 4:
Depreciation = (10/100) * $36,450 = $3,645
Value after Year 4 = $36,450 - $3,645 = $32,805
Year 5:
Depreciation = (10/100) * $32,805 = $3,280.50
Value after Year 5 = $32,805 - $3,280.50 = $29,524.50
Year 6:
Depreciation = (10/100) * $29,524.50 = $2,952.45
Value after Year 6 = $29,524.50 - $2,952.45 = $26,572.05
Year 7:
Depreciation = (10/100) * $26,572.05 = $2,657.20
Value after Year 7 = $26,572.05 - $2,657.20 = $23,914.85
Therefore, the value of the tractor after 7 years is approximately $23,914.85.