Let's solve the problem step-by-step.
### Part (a): Total Amount of Depreciation Allowed
Given data:
- Delivered price of the tractor: \[tex]$135,000
- Residual value percentage: 35%
- Useful life: 7,700 hours
First, calculate the residual value in dollars:
\[
\text{Residual value in dollars} = \text{Delivered price} \times \left(\frac{\text{Residual value percentage}}{100}\right) = 135,000 \times 0.35 = \$[/tex]47,250
\]
Next, calculate the total amount of depreciation allowed by subtracting the residual value from the delivered price:
[tex]\[
\text{Total depreciation} = \text{Delivered price} - \text{Residual value in dollars} = 135,000 - 47,250 = \$87,750
\][/tex]
Hence, the total amount of depreciation allowed is [tex]\( \$87,750 \)[/tex].
### Part (b): Amount of Depreciation Per Hour
To find the depreciation per hour, divide the total depreciation by the useful life in hours:
[tex]\[
\text{Depreciation per hour} = \frac{\text{Total depreciation}}{\text{Useful life in hours}} = \frac{87,750}{7,700} \approx \$11.40 \text{ (rounded to the nearest cent)}
\][/tex]
### Part (c): Depreciation for the First Year
The tractor is operated:
- 5 days a week
- An average of 7.25 hours per day
First, calculate the total number of hours the tractor is operated in a week:
[tex]\[
\text{Total hours per week} = 5 \times 7.25 = 36.25 \text{ hours}
\][/tex]
Next, calculate the total number of hours the tractor is operated in a year (assuming 52 weeks in a year):
[tex]\[
\text{Total hours per year} = 36.25 \times 52 = 1,885 \text{ hours}
\][/tex]
Finally, calculate the depreciation for the first year by multiplying the total hours operated in the first year by the depreciation per hour:
[tex]\[
\text{Depreciation for the first year} = \text{Total hours per year} \times \text{Depreciation per hour} = 1,885 \times 11.40 \approx \$21,481.66
\][/tex]
### Summary of Results
(a) Total amount of depreciation allowed: \[tex]$87,750
(b) Amount of depreciation per hour: \$[/tex]11.40
(c) Depreciation for the first year: \$21,481.66
