Answer:
1) Determine the machine's second-year depreciation and year end book value under the straight-line method.
depreciation expense per year = (purchase cost - salvage value) / useful life
depreciation expense per year = ($84,200 - $7,000) / 10 = $7,720
book value at the end of year 2 = $84,200 - ($7,720 x 2) = $68,760
2) Determine the machine's second-year depreciation using the double-declining-balance method.
depreciation year 1 = 2 x 1/10 x $84,200 = $16,840
depreciation year 2 = 2 x 1/10 x $67,360 = $13,472
book value at end of year 2 = $67,360 - $13,472 = $53,888