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Difficulty: MediumFinancial Mathematics (Interest, Profit, Loss, and Depreciation)

A logistics firm purchased a commercial delivery van for ₦800,000\text{₦}800,000. If the value of the van depreciates by 10%10\% in the first year and by 15%15\% in the second year, what is the value of the van at the end of the second year?

  1. ₦612,000\text{₦}612,000Answer
  2. B
    ₦600,000\text{₦}600,000
  3. C
    ₦188,000\text{₦}188,000
  4. D
    ₦648,000\text{₦}648,000

Answer

₦612,000\text{₦}612,000
To find the remaining value of an asset undergoing successive annual depreciation, multiply the initial cost by each annual retention factor (1−r)(1 - r). For Year 1 at 10%10\%, the value retention factor is 0.900.90, making the value ₦720,000\text{₦}720,000. For Year 2 at 15%15\%, the retention factor is 0.850.85, yielding a final value of ₦720,000×0.85=₦612,000\text{₦}720,000 \times 0.85 = \text{₦}612,000.

Step-by-Step Solution

1
Calculate the value of the van at the end of the first year after a 10% depreciation.
Value after Year 1=₦800,000×(1−10100)=₦800,000×0.90=₦720,000\text{Value after Year 1} = \text{₦}800,000 \times \left(1 - \frac{10}{100}\right) = \text{₦}800,000 \times 0.90 = \text{₦}720,000
Depreciation decreases the principal asset value by the specified percentage.
2
Calculate the value of the van at the end of the second year after a 15% depreciation on the year-one value.
Value after Year 2=₦720,000×(1−15100)=₦720,000×0.85=₦612,000\text{Value after Year 2} = \text{₦}720,000 \times \left(1 - \frac{15}{100}\right) = \text{₦}720,000 \times 0.85 = \text{₦}612,000
Successive depreciation is compounded on the reduced value at the start of each period.

Key Concept

Successive Asset Depreciation
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Topics

Financial Mathematics (Interest, Profit, Loss, and Depreciation)

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