The value of a machine depreciates by 10% every year. What is the total percentage depreciation after 2 years?

Question

The value of a machine depreciates by 10% every year. What is the total percentage depreciation after 2 years?

1. A. 21%
2. B. 20%
3. C. 19% (Correct answer)
4. D. 22%

Correct Answer

Option C — 19%

Detailed Solution & Explanation

The correct answer is 19%.

Shortcut Trick

• Two successive falls of 10% leave a multiplier of $0.9 \times 0.9 = 0.81$.
• The machine retains 81% of its value, so the total depreciation is $100 - 81 = \textbf{19\%}$.

Alternate Method

• Take the initial value as 100.
  • After year 1: $100 - 10 = 90$
  • After year 2: $90 - 10\% \text{ of } 90 = 90 - 9 = 81$
• Total fall $= 100 - 81 = 19$, i.e. 19%.

Additional Information

• The answer is not 20%, and that is the whole point of the question. The second year's 10% is charged on the *reduced* value of 90, not on the original 100 — so the second reduction is only 9.
• By the successive-change formula, $-10 - 10 + \dfrac{(-10)(-10)}{100} = -19\%$. The positive $+1$ term is why two 10% falls come to less than 20%.
• The same logic in reverse explains why two 10% rises give 21%, not 20% — depreciation and appreciation are symmetric in method but not in magnitude.