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4 votes
A certain car was purchased for $22,500. The car

has a resale value of $14,500 after a useful life of 6
years. What is the annual depreciation expense for
this car?
Annual depreciation expense = $ [?]
Round to the nearest hundredth.

2 Answers

6 votes

Answer: $1,333.33

Explanation:

User Thomas Ibbotson
by
4.3k points
9 votes


\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill &\$14500\\ P=\textit{initial amount}\dotfill &\$22500\\ r=rate\to r\%\to (r)/(100)\\ t=years\dotfill &6\\ \end{cases}


14500=22500(1 - (r)/(100))^(6)\implies \cfrac{14500}{22500}=\left( \cfrac{100-r}{100} \right)^6\implies \cfrac{29}{45}=\left( \cfrac{100-r}{100} \right)^6 \\\\\\ \sqrt[6]{\cfrac{29}{45}}=\cfrac{100-r}{100}\implies 100\sqrt[6]{\cfrac{29}{45}}=100-r \\\\\\ r=100-100\sqrt[6]{\cfrac{29}{45}}\implies r\approx \stackrel{\%}{7.06}

User Brian Silverman
by
4.9k points