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.
Well, it seems our farmer really dug himself a hole with that tractor! Let's calculate the value of his depreciating nightmare.
After the first year, the tractor would be worth 90% of its original value: $50,000 * 0.9 = $45,000.
The second year would bring it down another peg, to 90% of $45,000: $45,000 * 0.9 = $40,500.
Continuing this trend, we find that the value of the tractor keeps on sinking each year:
Year 3: $40,500 * 0.9 = $36,450
Year 4: $36,450 * 0.9 = $32,805
Year 5: $32,805 * 0.9 = $29,524.50
Year 6: $29,524.50 * 0.9 = $26,572.05
Year 7: $26,572.05 * 0.9 = $23,914.85
So after 7 years of tractor depreciation, our farming friend is left with a tractor worth approximately $23,914.85.
To find the value of the tractor in 7 years, we need to calculate its depreciation each year and subtract that amount from the original price.
Since the tractor depreciates 10% per year, we can calculate its depreciation for each year by multiplying the previous year's value by 0.10 (10% as a decimal).
Let's break down the calculation step by step:
Year 1:
Depreciation = $50,000 * 0.10 = $5,000
Value after Year 1 = $50,000 - $5,000 = $45,000
Year 2:
Depreciation = $45,000 * 0.10 = $4,500
Value after Year 2 = $45,000 - $4,500 = $40,500
Year 3:
Depreciation = $40,500 * 0.10 = $4,050
Value after Year 3 = $40,500 - $4,050 = $36,450
Year 4:
Depreciation = $36,450 * 0.10 = $3,645
Value after Year 4 = $36,450 - $3,645 = $32,805
Year 5:
Depreciation = $32,805 * 0.10 = $3,280.50
Value after Year 5 = $32,805 - $3,280.50 = $29,524.50
Year 6:
Depreciation = $29,524.50 * 0.10 = $2,952.45
Value after Year 6 = $29,524.50 - $2,952.45 = $26,572.05
Year 7:
Depreciation = $26,572.05 * 0.10 = $2,657.21
Value after Year 7 = $26,572.05 - $2,657.21 = $23,914.84
Therefore, the value of the tractor in 7 years would be approximately $23,914.84 rounded to the nearest penny.