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

Tushar Chandra | Certified Educator

calendarEducator since 2010

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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

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## Related Questions

kiran76 | Student

Many Thanks!

neela | Student

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.