1. **State the problem:** We know the car's value in 2021 is 16000 and it depreciates by 12.5% each year. We want to find its value in 2016. 2. **Formula used:** The value after $t$ years with depreciation rate $r$ is given by $$ V_t = V_0 (1 - r)^t $$ where $V_0$ is the initial value (in 2016), $V_t$ is the value after $t$ years, and $r=0.125$. 3. **Identify variables:** Here, $V_t = 16000$, $r=0.125$, and $t = 2021 - 2016 = 5$ years. 4. **Rearrange formula to find $V_0$:** $$ V_0 = \frac{V_t}{(1 - r)^t} $$ 5. **Calculate denominator:** $$ (1 - 0.125)^5 = 0.875^5 $$ 6. **Calculate $0.875^5$:** $$ 0.875^5 = 0.5132 \text{ (approx)} $$ 7. **Calculate initial value:** $$ V_0 = \frac{16000}{0.5132} $$ 8. **Simplify fraction:** $$ V_0 = 16000 \times \frac{1}{0.5132} \approx 16000 \times 1.948 = 31168 $$ **Answer:** The car was worth approximately $31168$ when first purchased in 2016.