Question

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question
a new car is purchased for 23700 dollars. the value of the car depreciates at 13.5% per year. what will the value of the car be, to the nearest cent, after 10 years?
answer attempt 1 out of 2
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Explanation:

Step1: Define depreciation formula

The exponential depreciation formula is $A = P(1-r)^t$, where $P$ is initial value, $r$ is annual depreciation rate, $t$ is time in years.

Step2: Plug in given values

$P=23700$, $r=0.135$, $t=10$. Substitute:
$A = 23700(1-0.135)^{10}$

Step3: Calculate remaining value factor

$1-0.135=0.865$. Compute $0.865^{10} \approx 0.1978$

Step4: Compute final value

$A = 23700 \times 0.1978 \approx 4687.86$

Answer:

$\$4687.86$