Car down

Sarah buys a car costing $12,500. It depreciates value by 8% in the first year, 10% in the second year, and 5% in the third year. Calculate the value of a car after the third year.

Correct answer:

x =  9832.5

Step-by-step explanation:

$$\begin{gathered} x_0=12500\text{USD} \\ {x}_1=(1-\frac{8}{100})\cdot x_0=(1-\frac{8}{100})\cdot 12500=11500\text{USD} \\ {x}_2=(1-\frac{10}{100})\cdot x_1=(1-\frac{10}{100})\cdot 11500=10350\text{USD} \\ {x}_3=(1-\frac{5}{100})\cdot x_2=(1-\frac{5}{100})\cdot 10350=\frac{19665}{2}=9832\frac{1}{2}=9832.5\text{USD} \\ x=x_3=\frac{19665}{2}=9832\frac{1}{2}=9832.5 \end{gathered}$$

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