9. A man bought a new trailer for $36,700. The insurance company decides to depreciate the trailer by 12.5% each year. Calculate the book value of the trailer at the end of 10 years.
Each year, the value of the trailer decreases by 12.5%, which is equivalent to multiplying the value by 0.875 (100% - 12.5% = 87.5%).
The book value of the trailer at the end of the first year is $36,700 * 0.875 = $<<36700*0.875=32012.50>>32,012.50.
Using the same formula, the book value at the end of the second year is $32,012.50 * 0.875 = $<<32012.50*0.875=28010.94>>28,010.94.
Continuing this calculation for 10 years, the book value at the end of the 10th year is:
$36,700 * (0.875)^10 = $10,804.32.
Therefore, the book value of the trailer at the end of 10 years is $10,804.32.
To calculate the book value of the trailer at the end of 10 years, we need to calculate the annual depreciation and subtract it from the original value.
Step 1: Calculate the annual depreciation.
The trailer depreciates by 12.5% each year. To calculate the annual depreciation, we can multiply the original value by 12.5% (0.125).
Annual depreciation = Original value * 0.125
Annual depreciation = $36,700 * 0.125
Annual depreciation = $4,587.50
Step 2: Calculate the remaining value at the end of each year.
To calculate the remaining value of the trailer at the end of each year, we need to subtract the annual depreciation from the original value.
Year 1: Remaining value = Original value - Annual depreciation
Remaining value = $36,700 - $4,587.50
Remaining value = $32,112.50
Year 2: Remaining value = Remaining value from Year 1 - Annual depreciation
Remaining value = $32,112.50 - $4,587.50
Remaining value = $27,525
Continue this process for 10 years.
Year 3: Remaining value = $27,525 - $4,587.50 = $22,937.50
Year 4: Remaining value = $22,937.50 - $4,587.50 = $18,350
Year 5: Remaining value = $18,350 - $4,587.50 = $13,762.50
Year 6: Remaining value = $13,762.50 - $4,587.50 = $9,175
Year 7: Remaining value = $9,175 - $4,587.50 = $4,587.50
Year 8: Remaining value = $4,587.50 - $4,587.50 = $0
Step 3: Calculate the book value at the end of 10 years.
At the end of 10 years, the book value of the trailer would be $0.
Therefore, the book value of the trailer at the end of 10 years is $0.