Final answer:
Using the sum-of-the-years'-digits method, the depreciation for 2025 would be $2,580, and the book value on December 31, 2025, would be $2,300.
Step-by-step explanation:
The sum-of-the-years'-digits method is used to calculate depreciation. It assumes that an asset's value diminishes more in the earlier years of its life. To calculate depreciation for 2025, we need to determine the fraction for that particular year. The equipment has a five-year life, so the sum of the digits is 15 (5 + 4 + 3 + 2 + 1). In 2025, the remaining life of the equipment is 1 year, so the fraction is 1/15. The depreciation for 2025 can be calculated by multiplying the depreciable cost (purchase cost - residual value) by the fraction. In this case, the depreciable cost is $42,000 - $3,300 = $38,700. Therefore, the depreciation for 2025 would be $38,700 * 1/15 = $2,580.
To calculate the book value on December 31, 2025, we need to subtract the accumulated depreciation from the initial cost. The accumulated depreciation can be calculated using the sum-of-the-years'-digits method. In this case:
Year 1: $38,700 * 5/15 = $12,900
Year 2: $38,700 * 4/15 = $10,320
Year 3: $38,700 * 3/15 = $7,740
Year 4: $38,700 * 2/15 = $5,160
Year 5: $38,700 * 1/15 = $2,580
Adding up all the depreciation, the accumulated depreciation on December 31, 2025, would be $39,700. Subtracting this from the initial cost, the book value on December 31, 2025, would be $42,000 - $39,700 = $2,300.