1. **State the problem:** We have a car purchased for 20700 dollars that depreciates at 13.75% per year. We want to find its value after 12 years. 2. **Formula used:** The value of an item depreciating exponentially is given by: $$ V = P(1 - r)^t $$ where: - $V$ is the value after $t$ years, - $P$ is the initial value, - $r$ is the depreciation rate (as a decimal), - $t$ is the time in years. 3. **Identify values:** - $P = 20700$ - $r = 0.1375$ - $t = 12$ 4. **Calculate:** $$ V = 20700(1 - 0.1375)^{12} $$ $$ V = 20700(0.8625)^{12} $$ 5. **Evaluate the power:** Calculate $0.8625^{12}$. 6. **Multiply:** $$ V = 20700 \times 0.1821 \approx 3769.47 $$ 7. **Final answer:** The value of the car after 12 years is approximately **3769.47** dollars.