Question

The value of a bike is Rs. 50,000. If the value depreciated by 5% in two years, find the value of the bike after 2 years.

Answer 1

Hint: In this question, we have to find the value of the bike after 2 years. This question is completely based on the formula. The formula which we are using is
Cost of bike after n years$ = {\text{initial price of bike}} \times {\left( {1 - \dfrac{{rate{\text{ }}of{\text{ }}depreciation}}{{100}}} \right)^n}$where n\[ = \]no. of years

Complete step-by-step solution:
Given: Initial price of bike \[ = \]Rs. 50,000
     Rate of depreciation$ = 5\% $
     Time $ = 2$years
Cost of bike after 2 years$ = {\text{initial price of bike}} \times {\left( {1 - \dfrac{{rate{\text{ }}of{\text{ }}depreciation}}{{100}}} \right)^n}$
On substituting the given values in the equation we get,
$ \Rightarrow Rs.50,000 \times {\left( {1 - \dfrac{5}{{100}}} \right)^2}$
On further simplification we get,
$ \Rightarrow Rs.50,000 \times \left( {\dfrac{{95 \times 95}}{{100 \times 100}}} \right)$
$ \Rightarrow \dfrac{{Rs.50,000 \times 9025}}{{10,000}}$
$ \Rightarrow Rs.5 \times 9025$
$ \Rightarrow Rs.45,125$
Therefore, the value of the bike after 2 years is Rs. 45,125.

Note: Depreciation means a reduction in the value of an asset over time. Many times this question can be asked for ‘n’ number of years so for that we have to use the above-mentioned formula by substituting the required values.
Additional Information: It is a Fact-Based Question.