# A car depreciates at a rate of 30% per year. How much will a $20000 car be worth after 5 years?

### 3 Answers | Add Yours

The car depreciates by 30% every year. So if its initial value is V, the next year it will be V*(1 - 30%) = V*(1 - 0.3) = V*0.7.

The year after that it will be V*(0.7)^2 and the value similarly decreases so that after n years it is equal to V*(0.7)^n.

Now, it is given that the initial value is $20,000. Therefore after 5 years it will be 20,000*(0.7)^5 = $3361.4

**The required value of the car is $3361.4**

The annual depreciation of the car is 30%.

So after the first year the car value is = $(20000-20000(30/100)} = $20000*(0.7).

At the end if the 2nd year, the car value after depreciation is $20000(0.7).

Similarlly at the end the 3rd , 4th and 5th years the car value becomes $20000*(0.7)^3 , $20000*(0.7)^4 and $2000*(0.7)^5 , respectively after depreciation.

Many Thanks!