A new truck was purchased for $58,000. Each year after the truck was purchased, its value decreased by approximately seven-eighths. What is the value of the truck 12 years after
it was purchased?
To find the value of the truck after 12 years, we need to apply the seven-eighths decrease to the original value each year. Let's set up an equation:
Value after 12 years = $58,000 x (7/8)^12
Simplifying, we get:
Value after 12 years = $58,000 x 0.028
Value after 12 years = $1,624
Therefore, the value of the truck 12 years after it was purchased is approximately $1,624.
To find the value of the truck 12 years after its purchase, we need to calculate its annual depreciation and subtract it from the original purchase price each year.
1. Calculate the annual depreciation:
Annual Depreciation = Original Value * Depreciation Rate
Depreciation Rate = 7/8
Annual Depreciation = $58,000 * (7/8) = $50,750
2. Calculate the value of the truck each year:
Year 1: Value = Purchase Price - Annual Depreciation = $58,000 - $50,750 = $7,250
Year 2: Value = Previous Year's Value - Annual Depreciation = $7,250 - $50,750 = -$43,500
Year 3: Value = Previous Year's Value - Annual Depreciation = -$43,500 - $50,750 = -$94,250
Year 4: Value = Previous Year's Value - Annual Depreciation = -$94,250 - $50,750 = -$145,000
Year 5: Value = Previous Year's Value - Annual Depreciation = -$145,000 - $50,750 = -$195,750
Year 6: Value = Previous Year's Value - Annual Depreciation = -$195,750 - $50,750 = -$246,500
Year 7: Value = Previous Year's Value - Annual Depreciation = -$246,500 - $50,750 = -$297,250
Year 8: Value = Previous Year's Value - Annual Depreciation = -$297,250 - $50,750 = -$348,000
Year 9: Value = Previous Year's Value - Annual Depreciation = -$348,000 - $50,750 = -$398,750
Year 10: Value = Previous Year's Value - Annual Depreciation = -$398,750 - $50,750 = -$449,500
Year 11: Value = Previous Year's Value - Annual Depreciation = -$449,500 - $50,750 = -$500,250
Year 12: Value = Previous Year's Value - Annual Depreciation = -$500,250 - $50,750 = -$551,000
Therefore, the value of the truck 12 years after its purchase is approximately -$551,000.
To find the value of the truck 12 years after it was purchased, we will need to calculate its depreciated value each year.
The truck's initial value is $58,000. Since its value decreases by approximately seven-eighths each year, we can calculate the value after one year using the formula:
Value after one year = Initial value - (Initial value * 7/8)
Substituting the values, we get:
Value after one year = $58,000 - ($58,000 * 7/8)
Value after one year = $58,000 - $50,375
Value after one year = $7,625
Now, we can continue this process for the remaining 11 years. We will use the value after one year as the new initial value and repeat the calculation for each subsequent year.
Value after two years = Initial value - (Initial value * 7/8)
Value after three years = Initial value - (Initial value * 7/8)
...
Value after twelve years = Initial value - (Initial value * 7/8)
After performing these calculations for each year, we can determine the value of the truck 12 years after it was purchased.