Question

The annual depreciation of a car's value is 10%. By what percentage will the price of the car fall after 4 years?
1. 34.39
2. 32.56
3. 40.12
4. 38.24

Answer 1

Correct Answer - Option 1 : 34.39

Given:

Annual depreciation of car value = 10%

Concept used:

If P is the initial price of the commodity, then after ‘n’ years the value of the commodity will become P × [1 – (n/100)]ⁿ

That means the new value of the commodity will be only [1 – (n/100)]ⁿ times the original price.

 Or, we can say, the value of price reduced by {1 – [1 – (n/100)]ⁿ} times the original price.

Calculation:

Percentage fall in price after 4 years = {1 – [1 – (10/100)]⁴} × 100

 Percentage fall in price after 4 years = [1 – (9/10)⁴] = [1 – 6561/10,000] × 100

Percentage fall in price after 4 years = 3439/10,000 × 100

We can see that, percentage fall in price after 4 years = 34.39%

∴ The percentage fall in price after 4 years is 34.39%.