Question

Difficulty: EasyPercent Change and Interest

A piece of industrial machinery valued at $\$5,000$ depreciates in value by $20\%$ during its first year of operation, and by $10\%$ of its reduced value during its second year. What is the value of the machinery, in dollars, at the end of the second year?

Answer: 3600 dollars

Answer

3600 dollars

Applying the successive percent reductions sequentially gives

\$5,000 \times 0.80 = \$4,000

at the end of Year 1, and

\$4,000 \times 0.90 = \$3,600

at the end of Year 2.

Step-by-Step Solution

1

Calculate the value after Year 1 depreciation

$4,000

Depreciation of 20% on $5,000 leaves 80% of the original value.

2

Calculate the value after Year 2 depreciation

$3,600

Depreciation of 10% on the new base of $4,000 leaves 90% of the Year 1 value.

Key Concept

Successive Percent Change

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Topics

Percent Change and Interest

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