Final answer:
To calculate the first year's depreciation using the double-declining-balance method, multiply the book value of $65,000 by the depreciation rate of 50%, resulting in a depreciation expense of $32,500 for the year ended December 31st, 2022.
Step-by-step explanation:
The equipment's book value at the beginning of the year is the cost minus any salvage value, which is $70,000 - $5,000 = $65,000. The double-declining-balance method of depreciation means we depreciate the asset at twice the straight-line rate. The straight-line depreciation rate is 1 divided by the useful life in years, which in this case is 1/4 or 25% per year. Therefore, the double-declining rate is 25% * 2 = 50% per year.
For the first year's depreciation, you multiply the book value by this rate. The calculation for the year ended December 31st, 2022, would then be $65,000 * 50% = $32,500 in depreciation expense.