The general equation for depreciation is given by [tex]$y=A(1-r)^t$[/tex], where [tex]$y=$[/tex] current value, [tex]$A=$[/tex] original cost, [tex]$r=$[/tex] rate of depreciation, and [tex]$t=$[/tex] time, in years. A car was purchased 6 years ago for [tex]$\$25,000$[/tex]. If the annual depreciation rate is 11%, which equation can be used to determine the approximate current value of the car?
[tex]$y=25,000(0.89)^6$[/tex]
[tex]$y=(25,000 \cdot 0.11)^6$[/tex]
[tex]$y=(25,000 \cdot 0.89)^6$[/tex]
[tex]$y=25,000(0.11)^6$[/tex]

Question

The general equation for depreciation is given by [tex]$y=A(1-r)^t$[/tex], where [tex]$y=$[/tex] current value, [tex]$A=$[/tex] original cost, [tex]$r=$[/tex] rate of depreciation, and [tex]$t=$[/tex] time, in years. A car was purchased 6 years ago for [tex]$\$25,000$[/tex]. If the annual depreciation rate is 11%, which equation can be used to determine the approximate current value of the car? 
[tex]$y=25,000(0.89)^6$[/tex] 
[tex]$y=(25,000 \cdot 0.11)^6$[/tex] 
[tex]$y=(25,000 \cdot 0.89)^6$[/tex] 
[tex]$y=25,000(0.11)^6$[/tex]

GinnyAnswer · Answer

Substitute the given values into the depreciation equation: y = A ( 1 − r ) t . 
 Plug in A = 25000 , r = 0.11 , and t = 6 into the equation: y = 25000 ( 1 − 0.11 ) 6 . 
 Simplify the expression inside the parentheses: 1 − 0.11 = 0.89 . 
 The equation becomes y = 25000 ( 0.89 ) 6 , which represents the approximate current value of the car: y = 25 , 000 ( 0.89 ) 6 ​ . 
 
 Explanation 
 
 Understanding the Problem We are given the general equation for depreciation: y = A ( 1 − r ) t , where: 
 
 y = current value A = original cost r = rate of depreciation t = time in years 
 We are given the following information: 
 A = $25 , 000 (original cost) r = 11% = 0.11 (annual depreciation rate) t = 6 years 
 We need to find the equation that determines the approximate current value of the car. 
 
 Substituting the values Substitute the given values into the depreciation equation: 
 
 y = A ( 1 − r ) t y = 25000 ( 1 − 0.11 ) 6 
 
 Simplifying the equation Simplify the expression inside the parentheses: 
 
 1 − 0.11 = 0.89 
 So the equation becomes: 
 y = 25000 ( 0.89 ) 6 
 
 Final Answer The equation that can be used to determine the approximate current value of the car is y = 25 , 000 ( 0.89 ) 6 . 
 
 Examples 
 Depreciation is a concept used in accounting and finance to allocate the cost of an asset over its useful life. For example, a company might purchase a machine for $10,000. Instead of expensing the entire $10,000 in the year of purchase, the company depreciates the machine over its useful life (e.g., 5 years). This means that each year, a portion of the machine's cost is recognized as an expense. The depreciation equation helps determine the remaining value of the asset at any point in time, which is important for financial reporting and decision-making. Understanding depreciation can help individuals and businesses make informed decisions about when to replace assets and how to manage their finances effectively.

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