To determine the depreciation that will be recorded during each of the remaining years of the useful life of the equipment, we need to follow these steps:
### Step 1: Calculate the Initial Annual Depreciation
Initially, the equipment cost [tex]$12,000, had a $[/tex]2,000 salvage value, and a useful life of 5 years. Using straight-line depreciation:
[tex]\[ \text{Initial Annual Depreciation} = \frac{\text{Cost of Equipment} - \text{Initial Salvage Value}}{\text{Initial Useful Life}} \][/tex]
[tex]\[ \text{Initial Annual Depreciation} = \frac{12,000 - 2,000}{5} = \frac{10,000}{5} = \$2,000 \][/tex]
### Step 2: Calculate the Accumulated Depreciation by the Beginning of Year 4
By the beginning of Year 4, the equipment has been depreciated for 3 years.
[tex]\[ \text{Accumulated Depreciation} = \text{Initial Annual Depreciation} \times (\text{Years Used}) \][/tex]
[tex]\[ \text{Accumulated Depreciation} = 2,000 \times 3 = \$6,000 \][/tex]
### Step 3: Determine the Book Value at the Beginning of Year 4
The book value at the beginning of Year 4 is the cost of the equipment minus the accumulated depreciation:
[tex]\[ \text{Book Value at Beginning of Year 4} = \text{Cost of Equipment} - \text{Accumulated Depreciation} \][/tex]
[tex]\[ \text{Book Value at Beginning of Year 4} = 12,000 - 6,000 = \$6,000 \][/tex]
### Step 4: Calculate the Remaining Useful Life
The total useful life has been revised to 6 years. Since 3 years have already passed:
[tex]\[ \text{Remaining Useful Life} = \text{Revised Total Useful Life} - \text{Years Used} \][/tex]
[tex]\[ \text{Remaining Useful Life} = 6 - 3 = 3 \][/tex]
### Step 5: Calculate the Revised Annual Depreciation
With the new salvage value of [tex]$1,200 and a remaining useful life of 3 years, we need to revise the annual depreciation:
\[ \text{Revised Annual Depreciation} = \frac{\text{Book Value at Beginning of Year 4} - \text{Revised Salvage Value}}{\text{Remaining Useful Life}} \]
\[ \text{Revised Annual Depreciation} = \frac{6,000 - 1,200}{3} = \frac{4,800}{3} = \$[/tex]1,600 \]
### Conclusion:
The amount of depreciation that will be recorded during each of the remaining years of the equipment's useful life is:
[tex]\[ \boxed{\$1,600} \][/tex]
