Question

A new car is purchased for $\$16,200$. The value of the car depreciates at $14.25\%$ $peryear$. What will the value of the car be, to the nearest cent, after $6$ $years$?

Answer 1

Finding the value of the car after $6$ $years$.

Given, that the value of the car is depreciating at the rate of $14.25\%$.

Also, the cost of the car initially, $\mathrm{P}=\$16,200$.

Therefore, the value of the car after $6$ $years$ $=P{\left(1-r\right)}^t$ where, $\mathrm{t}$ is the period of the time in $years$.

$$\begin{gathered} =16200{\left(1-\frac{14.25}{100}\right)}^6 \\ =16,200{\left(1-0.1425\right)}^6 \\ =\$6,440.503 \end{gathered}$$

Hence, the value of the car after $6$ $years$ when the rate of depreciation is $14.25\%$ and the original value of the car is $\$16,200$, is $\$6,440.5$.