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Math  /  Data & Statistics

QuestionA scooter is purchased for $4,000\$ 4,000 and has a resale value of $200\$ 200 after a useful life of 5 years. Using a book value depreciation chart, calculate the number of years until the book value of the scooter is $2,480\$ 2,480. [?] years Enter

Studdy Solution

STEP 1

1. The scooter depreciates linearly over its useful life.
2. The initial cost of the scooter is \$4,000.
3. The resale value after 5 years is \$200.
4. We need to find the number of years until the book value is \$2,480.

STEP 2

1. Determine the annual depreciation.
2. Calculate the book value after each year.
3. Determine the number of years until the book value is \$2,480.

STEP 3

Calculate the total depreciation over the useful life:
Total Depreciation=Initial Cost−Resale Value=4000−200=3800 \text{Total Depreciation} = \text{Initial Cost} - \text{Resale Value} = 4000 - 200 = 3800

STEP 4

Calculate the annual depreciation:
Annual Depreciation=Total DepreciationUseful Life=38005=760 \text{Annual Depreciation} = \frac{\text{Total Depreciation}}{\text{Useful Life}} = \frac{3800}{5} = 760

STEP 5

Calculate the book value after each year until it reaches \$2,480:
- Year 0: Book Value = \$4,000 - Year 1: Book Value = \$4,000 - \$760 = \$3,240 - Year 2: Book Value = \$3,240 - \$760 = \$2,480

STEP 6

Determine the number of years until the book value is \$2,480:
The book value reaches \$2,480 after 2 years.
The number of years is:
2 \boxed{2}

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