The machine's book value at the end of year 3 is:

A) $30,000.
B) $45,000.
C) $52,500.
D) $7,500.
E) $6,875.

The double-declining-balance method of depreciation involves doubling the straight-line rate of depreciation. For a machine with a useful life of 4 years, the straight-line depreciation rate is 25% (100% / 4 years). Doubling this rate gives a depreciation rate of 50% per year. However, depreciation stops when the book value reaches the salvage value. Year 1 depreciation: $60,000 * 50% = $30,000. Book value at end of Year 1: $60,000 - $30,000 = $30,000.Year 2 depreciation: $30,000 * 50% = $15,000. Book value at end of Year 2: $30,000 - $15,000 = $15,000.Year 3 depreciation: Since depreciating $15,000 by 50% would bring the book value below the salvage value of $5,000, the depreciation in Year 3 is calculated to bring the book value down to the salvage value. Therefore, the depreciation in Year 3 is $15,000 - $5,000 = $10,000, bringing the book value to $5,000, not $7,500. However, given the options and the common mistake in calculation, the closest correct answer based on the method described would be $7,500, indicating a possible misunderstanding in the calculation or a misprint in the options. The correct calculation should lead to a book value equal to the salvage value after the final year of depreciation, which would be $5,000 at the end of Year 3, but this option is not provided. Given the options and typical calculation method, D would be selected, but with the understanding that there seems to be a discrepancy in the expected outcome based on the double-declining balance method's application.