A vehicle purchased for $\$ 29,800$ depreciates at a constant rate of $5 \%$. Determine the approximate value of the vehicle 13 years after purchase. Round to the nearest whole dollar.

Step 1 ：The problem provides that a vehicle was purchased for $29,800 and depreciates at a constant rate of 5% per year. We are asked to determine the approximate value of the vehicle 13 years after purchase.

Step 2 ：We can model the depreciation of the vehicle's value with the formula \(V = P * (1 - r)^t\), where \(V\) is the final value, \(P\) is the initial value, \(r\) is the rate of depreciation, and \(t\) is the time in years.

Step 3 ：Given that \(P = \$29,800\), \(r = 5% = 0.05\), and \(t = 13\) years, we can substitute these values into the formula.

Step 4 ：Doing so, we find that \(V = \$29,800 * (1 - 0.05)^{13}\).

Step 5 ：Calculating the above expression, we find that \(V = \$15,298\).

Step 6 ：Thus, the approximate value of the vehicle 13 years after purchase is \(\boxed{\$15,298}\).