Questions: A vehicle purchased for 29,800 depreciates at a constant rate of 4%. Determine the approximate value of the vehicle 13 years after purchase. Round to the nearest whole dollar.

A vehicle purchased for 29,800 depreciates at a constant rate of 4%. Determine the approximate value of the vehicle 13 years after purchase. Round to the nearest whole dollar.

Transcript text: A vehicle purchased for $\$ 29,800$ depreciates at a constant rate of $4 \%$. Determine the approximate value of the vehicle 13 years after purchase. Round to the nearest whole dollar. \$ Check Answer

Solution

Solution Steps

Step 1: Understand the Problem

We are given the initial purchase price $P$ of a vehicle, its annual depreciation rate $r\% $, and the number of years $V$ after the purchase for which we want to determine the value of the vehicle.

Step 2: Apply the Formula

The value of the vehicle after $V$ years can be calculated using the formula for exponential decay due to constant rate depreciation: \[A = P \times (1 - \frac{r}{100})^V\] Where:

$A$ is the approximate value of the vehicle after $V$ years.
$P$ is the initial purchase price of the vehicle.
$r$ is the annual depreciation rate.
$V$ is the number of years after the purchase.

Step 3: Substitute the Values and Calculate

Substituting the given values $P = 29800$, $r = 4\% $, and $V = 13$ years into the formula, we get: \[A = 29800 \times (1 - \frac{4}{100})^{13} = 17528\]