Question

Dinesh purchased a scooter for 24000. The value of the scooter is depreciating at the rate of 5% per annum. Calculate its value after 3 years.

Answer 1

Hint: In this question, we are given the price of a scooter. We know that the value of all the purchased things decreases with time, so the value of this scooter also decreases as time passes. We are given that the depreciation rate is 5% per annum, that is, the value of the scooter decreases by 5% every year. We can find the value of the scooter after 3 years by using the formula for calculating the price of something after “n” years.

Complete step-by-step answer:
The value of scooter after “n” years is calculated by the formula,
 $ A = P{(1 + \dfrac{r}{{100}})^n} $ , where $ A = $ final amount, $ P = $ the amount borrowed, $ r = $ interest and $ n = $ number of periods.
We know that the scooter was bought for 24000. So the principal value $ P = 24000 $ , $ r = - 5\% $ and $ n = 3 $
Put the known values in the given above equation,
 $
  A = 24000{(1 - \dfrac{5}{{100}})^3} \\
   \Rightarrow A = 24000{(\dfrac{{95}}{{100}})^3} \\
   \Rightarrow A = 24000 \times \dfrac{{95}}{{100}} \times \dfrac{{95}}{{100}} \times \dfrac{{95}}{{100}} \\
   \Rightarrow A = 20577 \;
  $
Hence, the value of the scooter bought for 24000 depreciating at the rate of 5% per annum after 3 years is 20577.
So, the correct answer is “Rs.20577”.

Note: The formula used is also used to calculate the sum of money that has to be paid by someone after “n” years when it is borrowed at r% compound interest. In the case of compound interest, we calculate the interest for the first period and then add it to the amount borrowed, then calculate the interest for the next period using the new amount and so on.