91Ó°ÊÓ

To find the straight-line depreciation rate, divide 100% by the number of years in the depreciation period: $$ \text{Depreciation rate} = \frac{100\%}{\text{Depreciation period}} $$ For this problem, the depreciation period is 10 years. So the straight-line depreciation rate is: $$ \text{Depreciation rate} = \frac{100\%}{10} = 10\% $$

To find the double declining-balance depreciation rate, we simply double the straight-line depreciation rate: $$ \text{Double declining-balance rate} = 2 \times \text{Straight-line depreciation rate} $$ In this case, the straight-line depreciation rate is 10%. So the double declining-balance depreciation rate is: $$ \text{Double declining-balance rate} = 2 \times 10\% = 20\% $$

To calculate the depreciation amount for each year, we multiply the double declining-balance depreciation rate by the remaining value of the office equipment at the beginning of each year. $$ \text{Depreciation amount for year n} = \text{Remaining value at the beginning of year n} \times \text{Double declining-balance rate} $$ We will calculate the depreciation amount for each of the first seven years.

To calculate the book value at the end of the 7th year, subtract the accumulated depreciation amount from the initial cost of the office equipment: $$ \text{Book value} = \text{Initial cost} - \text{Accumulated depreciation amount} $$ We will compute the accumulated depreciation amount at the end of the 7th year and then find the book value.

Now, we compute the depreciation amount for each year and the book value at the end of the 7th year: Initial cost = $80,000 \\ Double declining-balance rate = 20\% Year 1: \\ Depreciation amount = $80,000 \times 20\% = \$16,000 \\ Remaining value = \(80,000 - \$16,000 = \)64,000 Year 2: \\ Depreciation amount = $64,000 \times 20\% = \$12,800 \\ Remaining value = \(64,000 - \$12,800 = \)51,200 Year 3: \\ Depreciation amount = $51,200 \times 20\% = \$10,240 \\ Remaining value = \(51,200 - \$10,240 = \)40,960 Year 4: \\ Depreciation amount = $40,960 \times 20\% = \$8,192 \\ Remaining value = \(40,960 - \$8,192 = \)32,768 Year 5: \\ Depreciation amount = $32,768 \times 20\% = \$6,553.60 \\ Remaining value = \(32,768 - \$6,553.60 = \)26,214.40 Year 6: \\ Depreciation amount = $26,214.40 \times 20\% = \$5,242.88 \\ Remaining value = \(26,214.40 - \$5,242.88 = \)20,971.52 Year 7: \\ Depreciation amount = $20,971.52 \times 20\% = \$4,194.30 \\ Remaining value = \(20,971.52 - \$4,194.30 = \)16,777.22 Therefore, the book value of the office equipment at the end of the 7th year is $16,777.22.