Depreciation · Hook

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Ever wondered why a used keke costs less than a new one?

Aisha's uncle bought a new keke for ₦2,500,000. After a few years of carrying passengers on rough roads, nobody will pay that price for it. The fall in value over time is called depreciation.

Revision notes

📒 Depreciation: lesson notes

Work out how much a car, keke or laptop loses in value each year, by the straight-line and reducing-balance methods.

Aisha's uncle bought a new keke for ₦2,500,000. After a few years of carrying passengers on rough roads, nobody will pay that price for it. The fall in value over time is called depreciation.

Straight-line depreciation

Depreciation is the loss in value of an item as it gets older and wears out.

In the straight-line method the item loses the same amount every year: (cost − value at the end) ÷ number of years.

A laptop costs ₦500,000 and is sold for ₦100,000 after 4 years: (₦500,000 − ₦100,000) ÷ 4 = ₦100,000 per year.

🔑 Key idea: Straight-line: the same amount is lost every year.

Reducing-balance depreciation

In the reducing-balance method the item loses a fixed percentage of its current value each year.

A car worth ₦2,000,000 depreciates at 20% a year: year 1 → ₦1,600,000; year 2: 20% of ₦1,600,000 = ₦320,000, leaving ₦1,280,000.

It is like compound interest going down: V = P(1 − r/100)n = ₦2,000,000 × 0.82 = ₦1,280,000.

🔑 Key idea: V = P(1 − r/100)n

Total depreciation

Total depreciation = cost − value now. For the car: ₦2,000,000 − ₦1,280,000 = ₦720,000.

Taking 20% of the ORIGINAL price twice would give ₦800,000 — that is the straight-line mistake. On the reducing balance, each year's drop is smaller than the last.

🔑 Key idea: Total depreciation = original cost − current value.

Worked example

Yusuf buys a keke (tricycle) for ₦2,480,000. It depreciates by 20% per annum on the reducing balance. Find its value after 3 years.

  1. Step 1: Year 1

    ₦2,480,000 − 20% of ₦2,480,000 = ₦2,480,000 − ₦496,000 = ₦1,984,000

    Why? Each year the value drops by r% of what it was worth at the START of that year.

  2. Step 2: Year 2

    ₦1,984,000 − 20% of ₦1,984,000 = ₦1,984,000 − ₦396,800 = ₦1,587,200

  3. Step 3: Year 3

    ₦1,587,200 − 20% of ₦1,587,200 = ₦1,587,200 − ₦317,440 = ₦1,269,760

  4. Step 4: Formula check

    V = ₦2,480,000 × (1 − 20100)3 = ₦1,269,760

Answer: ₦1,269,760

Summary

  • Depreciation is loss of value over time.
  • Straight-line: (cost − end value) ÷ years, the same every year.
  • Reducing balance: V = P(1 − r/100)n.
  • Total depreciation = cost − current value.

Ready to check you've got it? Scroll up and work through the lesson: the interactive visuals, practice questions and mastery check are all there.