A construction company buys a bulldozer for $26,000. The company expects the useful life of the machine to be 12 years, at which time its value will have depreciated to $6000. The company uses the declining balances method for depreciation, so the annual depreciation rate r (in decimal form) is given by the formula r=1 - (S/C) ^1/n. In the formula, n is the useful life of the item (in years), S is the salvage value (in dollars), and C is the original cost (in dollars). What annual depreciation rate (in percent form) did the company use? Round your answer to the nearest tenth.

Question

Mathematics

Cody Estes

19 May, 22:59

A construction company buys a bulldozer for $26,000. The company expects the useful life of the machine to be 12 years, at which time its value will have depreciated to $6000. The company uses the declining balances method for depreciation, so the annual depreciation rate r (in decimal form) is given by the formula r=1 - (S/C) ^1/n. In the formula, n is the useful life of the item (in years), S is the salvage value (in dollars), and C is the original cost (in dollars). What annual depreciation rate (in percent form) did the company use? Round your answer to the nearest tenth.

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Answers (1)

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Elsa Simpson · Answer 1

11.5%

Step-by-step explanation:

Put the given numbers in the formula and do the arithmetic.

r = 1 - (6000/26000) ^ (1/12) = 1 - (3/13) ^ (1/12) ≈ 1 - 0.88498 ≈ 11.5%

The company used a depreciation rate of 11.5%.