CMA Foundation · Fundamentals of Business Mathematics and Statistics · Time Value of Money and Annuity - Simple and Compound Interest
A company buys equipment for Rs 1,00,000 and depreciates it by the diminishing balance method at a constant rate. After 2 years the book value is Rs 64,000. What is the annual rate of depreciation?
The rate is 20% per annum. Under the diminishing balance method the book value is cost times (1 minus rate) squared, so 0.64 means 1 minus rate is 0.8. Simply averaging the 36% fall as 18% a year is wrong.
- A16%
- B18%
- C20%Correct
- D25%
Explanation
Let rate be r. 1,00,000 x (1 - r)^2 = 64,000, so (1 - r)^2 = 0.64 and 1 - r = 0.8, giving r = 20%. Check: 1,00,000 x 0.8 x 0.8 = 64,000. The straight line view of 36% over 2 years gives 18%, which is wrong because depreciation is on the reducing balance.
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