Question

You buy a car for 1000 every year it loses 40% of its value

Answer 1

Answer:

$\displaystyle V_n=V_o\left(0.60\right)^n$

The car is worth 360 after two years

Step-by-step explanation:

Model For Depretiation

Assume the situation of something that has an initial value Vo and loses its value by a x% every year. The first year it will lose

$\displaystyle \frac{xV_o}{100}$

and it will have a new value of

$\displaystyle V_1=V_o-x\frac{V_o}{100}=V_o\left(\frac{100-x}{100}\right)$

Next year it will have a value of

$\displaystyle V_2=V_o\left(\frac{100-x}{100}\right)^2$

Since x=40%, we can deduct the general formula

$\displaystyle V_n=V_o\left(0.60\right)^n$

For n=2

$\displaystyle V_2=1000\left(0.60\right)^2$

$V_2=360$