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A car was valued at $38,000 in the year 2007. By 2013, the value had depreciated to $11,000. If the car's value continues to drop by the same percentage, what will it be worth by 2017?

User Ardin
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1 Answer

6 votes

From the depreciation formula:


A=P(1-(r)/(100))^n

we know the final value A=$11,000, the initial values P=$38000 and the number of years n=6. Then, we need to find the rate r. By substituting these values into the formula, we have


11000=38000(1-(r)/(100))^6

Then, by dividing both sides by 38000, we get


\begin{gathered} (11000)/(38000)=(1-(r)/(100))^6 \\ or\text{ equivalently,} \\ (1-(r)/(100))^6=0.28947 \end{gathered}

Now, by applying 6th root to both sides, we have


(1-(r)/(100))=0.813332

by subtracting 1 to both sides, we have


-(r)/(100)=-0.186667

or equivalently,


(r)/(100)=0.186667

Then, the rate is given by


\begin{gathered} r=100*0.186667 \\ r=18.6667\text{ \%} \end{gathered}

Once we know the rate, we can find the car's value by 2017. Then, we have


A=38000(1-(18.667)/(100))^(10)

where n=10 years (from 2007 to 2017). By computing the term into the paranthesis, we have


\begin{gathered} A=38000(1-0.18667)^(10) \\ A=38000(0.813332)^(10) \end{gathered}

which gives


\begin{gathered} A=38000(0.12667) \\ A=4813.549 \end{gathered}

Therefore, the answer is $4813.549

User Gregor Sklorz
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