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 need to calculate its depreciation each year and subtract it from the original price.
The tractor depreciates by 10% each year, which means it retains 90% (100% - 10%) of its value each year.
Step 1: Calculate the depreciation in the first year.
The value of the tractor after 1 year would be 90% of the original price ($50,000):
Value after 1 year = $50,000 * 0.90
Value after 1 year = $45,000
Step 2: Calculate the depreciation in the second year.
Similarly, the value after 2 years would be 90% of the value after 1 year:
Value after 2 years = $45,000 * 0.90
Value after 2 years = $40,500
Step 3: Continue this process for each year until we reach 7 years:
Year 3: $40,500 * 0.90 = $36,450
Year 4: $36,450 * 0.90 = $32,805
Year 5: $32,805 * 0.90 = $29,524.50
Year 6: $29,524.50 * 0.90 = $26,572.05
Year 7: $26,572.05 * 0.90 = $23,914.85
So, the value of the tractor after 7 years, rounded to the nearest penny, is $23,914.85.