Question

The cost of a vehicle is Rs. 1,75,000. If its value depreciates at the rate of \[20\% \] per annum, then the total depreciation after 3 years was
A. Rs. 86,400
B. Rs. 82,500
C. Rs. 84,500
D. Rs. 85,400

Answer 1

Hint: We know that, if the rate of depreciation is r % per year and the initial value of the asset is P, the depreciated value at the end of n years is given by $p{\left( {1 - \dfrac{r}{{100}}} \right)^n}$. Therefore the amount of depreciation is the initial value of the asset minus the depreciated value at the end of n years. Now the cost of the vehicle and the rate of depreciation per annum is given. Hence one can easily find the total depreciation after 3 years.

Complete step by step answer:

The cost of the vehicle (P) is Rs. 1,75,000
Given that, its value depreciates at the rate of \[20\% \] per annum.
Now,
Time (n) is 3 years
Rate of depreciation (r) is \[20\% \]
We know, depreciated value at the end of n years$ = p{\left( {1 - \dfrac{{rate}}{{100}}} \right)^{time}}$
Therefore amount after 3 years will be:
$p{\left( {1 - \dfrac{r}{{100}}} \right)^n}$
On substituting the values of p, r and t, we get,
\[ = 175000 \times {\left( {1 - \dfrac{{20}}{{100}}} \right)^3}\]
On simplification we get,
\[ = 175000 \times {\left( {\dfrac{4}{5}} \right)^3}\]
On expanding the cube we get,
\[ = 175000 \times \dfrac{4}{5} \times \dfrac{4}{5} \times \dfrac{4}{5}\]
On further simplification we get,
\[ = 1400 \times 64\]
\[ = Rs.89600\]
Hence, total depreciation after 3 years is given by
\[ = \]initial price \[ - \] depreciated value after 3 years
$ = 175000 - 89600$
$ = Rs.85400$
Hence, the total depreciation after 3 years is Rs. 85400.
Hence, the correct option is (C).

Note: Depreciation is the term used to describe this decrease in book value of an asset. There are a number of methods of calculating depreciation. The most common method is called the Diminishing Balance Method/ Reducing Instalment Method. Here as the book value decreases every year, the amount of depreciation also decreases by the end of the year. If the rate of depreciation is r % per year and the initial value of the asset is P, the depreciated value at the end of n years is given by $p{\left( {1 - \dfrac{r}{{100}}} \right)^n}$
The amount of depreciation is
$ = p - p{\left( {1 - \dfrac{r}{{100}}} \right)^n}$
$ = p\left[ {1 - {{\left( {1 - \dfrac{r}{{100}}} \right)}^n}} \right]$