#### Explanation:

Let ${a}_{1} = 30 , 000$ be the car's initial value, We knwo, that every year the new value can be calculated as:

${a}_{n + 1} = {a}_{n} \cdot \left(1 - 0.15\right) = 0.85 {a}_{n}$

From this we know, that the consecutive values form a (decreasing) geometric sequence with: a_1=$30,000, $q = 0.85$, and every term ${a}_{i}$(for $i \ge 2$) is the car's value after year number $i - 1$, so the value we are looking for is ${a}_{5}$${a}_{5} = {a}_{1} \cdot {q}^{5 - 1} = {a}_{1} \cdot {q}^{4} = 30 , 000 \cdot {\left(0.85\right)}^{4} \approx 15 , 660.19\$