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A car normally depreciates 30% of its original value in the first year. A car is worth $11,466...

Question:

A car normally depreciates 30% of its original value in the first year. A car is worth $11,466 after the first year.

What was its original value?

Depreciation:

Depreciation is defined as the loss in value of a fixed asset, such as a motor vehicle or furniture. Normally, the depreciation rate is stated in percentage terms. For example, if furniture depreciates at the rate of 10% per year and its value this year is $150, then the value of this asset in the next year will be 90% of its current value which is {eq}\dfrac{90}{100}\times \$150 = \$135 {/eq}.

Answer and Explanation:


Let the original value of the car be {eq}y {/eq}.

If a car depreciates 30% of its original value in the first year, and the car is worth $11,466 after the first year, then this means that this value is 70% of the original value. Therefore:

  • {eq}\dfrac{70}{100}x = \$11,466 {/eq}

Solving for x:

  • {eq}x = \dfrac{\$11,466\times 100}{70} {/eq}
  • {eq}x = \$16,380 {/eq}

The original value of the car is {eq}\boxed{\color{blue}{\$16,380}} {/eq}


Learn more about this topic:

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Straight-Line Depreciation: Method, Formula & Example

from Corporate Finance: Help & Review

Chapter 8 / Lesson 2
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