A machine valued at N20,000 depreciates by 10% every year. What will be the value of the machine at the end of two years?

Analyze the question: A machine worth N20,000 loses 10% of its value each year. We need its value after 2 years. Since the depreciation is 10% of the current value each year (not of the original value), this is a reducing-balance (compound) depreciation problem.

Concept: Value after n years = Original value × (1 − r/100)ⁿ

Here, the original value is N20,000, the rate r = 10%, and n = 2.

Solution:

Year 1:

• Depreciation = 10% of 20,000 = N2,000
• Value = 20,000 − 2,000 = N18,000

Year 2:

• Depreciation = 10% of 18,000 = N1,800
• Value = 18,000 − 1,800 = N16,200

Check with the formula: Value = 20,000 × (0.9)² = 20,000 × 0.81 = N16,200

Answer: N16,200, which is option A.

Common mistake to avoid: If you subtracted 10% of the original value twice (20,000 − 4,000), you would get N16,000. That is simple depreciation, and it is not an option here. The question says "every year," so the 10% applies to the new reduced value each time.

Exam tip: For depreciation, multiply by (1 − rate) each year. A 10% fall means multiplying by 0.9 each time, so two years means ×0.9 × 0.9 = ×0.81. For growth (like compound interest), multiply by (1 + rate) instead.