Question

A scooter was bought at Rs 42,000. Its value depreciated at the rate of 8% per annum. Find its value after one year?
A. Rs. 38640
B. Rs. 37740
C. Rs. 38154
D. Rs. 39640

Answer 1

In the given question, we have been asked the depreciated value of the scooter after 1 year and it is given that the scooter is depreciated at the rate of 8% per annum. In order to solve the question, with the help of depreciation formula when the rate is compounded i.e.$A=P{{\left( 1+\dfrac{R}{100} \right)}^{n}}$, we will easily find the depreciated value of scooter after a year by putting all the given values in the question.

Formula used:
$A=P{{\left( 1+\dfrac{R}{100} \right)}^{n}}$, where A is the amount, P is the principal amount or the initial amount, R is the given rate and ‘n’ is the number of years.

Complete step by step answer:
Complete step by step solution:
We have given that,
Scooter was bought for Rs 42,000 i.e.
Principal amount = P = 42,000
Here,
Rate of depreciation = 8% per annum
Depreciation means the value of an asset decreases.
So, we will use the negative sign with a tear of depreciation. i.e.
Rate = -8%
We know that,
To find the final amount we will use the formula i.e.
$A=P{{\left( 1+\dfrac{R}{100} \right)}^{n}}$, where A is the amount, P is the principal amount or the initial amount, R is the given rate and ‘n’ is the number of years.
Here, in this question;
A = to be find
P = 42,000
R = -8% p.a.
n = 1 year
Putting the values in the formula, we get
$\Rightarrow A=42,000{{\left( 1+\dfrac{\left( -8 \right)}{100} \right)}^{1}}$
Simplifying the above expression, we get
$\Rightarrow A=42,000{{\left( 1-\dfrac{8}{100} \right)}^{1}}$
Simplifying the numbers in the bracket by taking LCM, we obtained
$\Rightarrow A=42,000\left( \dfrac{100-8}{100} \right)=42,000\times \left( \dfrac{92}{100} \right)$
Cancelling out the common terms, we get
$\Rightarrow A=420\times 92=38,640$
Therefore,
$\Rightarrow A=38,640$
Thus, the value of scooter after one year is Rs 38,640.

So, the correct answer is Option A.

Note: To solve these types of questions, students need to remember the concept of calculating the depreciation amount. In the given question, we have been only asked the amount of scooter after one year. If they asked the amount after 2 years of more than 2 years then we need to remember that the rate given is compounded annually that means depreciated value after the second year is calculated on the basis of depreciated value of a given machine or asset after the first year.