Question

The cost of a vehicle is Rs. 1,75,000. If its value depreciates at the rate of $$20\mathrm{\%}$$ 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 $p{\left(1-{\displaystyle \frac{r}{100}}\right)}^n$. 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 $$20\mathrm{\%}$$ per annum.
Now,
Time (n) is 3 years
Rate of depreciation (r) is $$20\mathrm{\%}$$
We know, depreciated value at the end of n years$=p{\left(1-{\displaystyle \frac{rate}{100}}\right)}^{time}$
Therefore amount after 3 years will be:
$p{\left(1-{\displaystyle \frac{r}{100}}\right)}^n$
On substituting the values of p, r and t, we get,
$$=175000\times {\left(1-{\displaystyle \frac{20}{100}}\right)}^3$$
On simplification we get,
$$=175000\times {\left({\displaystyle \frac{4}{5}}\right)}^3$$
On expanding the cube we get,
$$=175000\times {\displaystyle \frac{4}{5}}\times {\displaystyle \frac{4}{5}}\times {\displaystyle \frac{4}{5}}$$
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 $p{\left(1-{\displaystyle \frac{r}{100}}\right)}^n$
The amount of depreciation is
$=p-p{\left(1-{\displaystyle \frac{r}{100}}\right)}^n$
$=p\left[1-{\left(1-{\displaystyle \frac{r}{100}}\right)}^n\right]$