Question

Calculate the compound interest for the third year on $ Rs.7500 $ invested for 5 years at $ 10\% $ per annum.
A. $ Rs.907.50 $
B. $ Rs.2482.50 $
C. $ Rs.2582.50 $
D. $ Rs.982.50 $

Answer 1

Hint: To solve this problem, we need to use the formula for compound interest. We will first find the final amount for the third year and then for the second year. Finally, we will find the difference between the final amount of third year and second year which will be the compound interest for the third year.
Formula used:
 $ A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T} $ , where, $ A $ is the final amount, $ P $ is the principal amount, $ R $ is the rate of interest and $ T $ is the time period

Complete step-by-step answer:
To find the compound interest for the third year, we first need to find the final amounts of second and third year.
First, we will find the final amount of the second year.
We know that final amount is given by
 $ A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T} $
In this formula we will put $ P $ = $ Rs.7500 $ , $ R = 10\% $ and $ T = 2years $
 $
   \Rightarrow A = 7500{\left( {1 + \dfrac{{10}}{{100}}} \right)^2} \\
   \Rightarrow A = 7500 \times \dfrac{{110}}{{100}} \times \dfrac{{110}}{{100}} \\
   \Rightarrow A = 75 \times 121 \\
   \Rightarrow A = Rs.9075 \;
  $
Now, we will find the final amount of the third year.
We will take $ P $ = $ Rs.7500 $ , $ R = 10\% $ and $ T = 3years $

 $
   \Rightarrow A = 7500{\left( {1 + \dfrac{{10}}{{100}}} \right)^3} \\
   \Rightarrow A = 7500 \times \dfrac{{110}}{{100}} \times \dfrac{{110}}{{100}} \times \dfrac{{110}}{{100}} \\
   \Rightarrow A = 75 \times 121 \times 1.1 \\
   \Rightarrow A = Rs.9982.50 \;
  $
Now, for finding the compound interest for the third year, we will subtract the final amount of the second year from the final amount of the third year.
Therefore, compound interest for the third year $ = Rs.9982.50 - Rs.9075 = Rs.907.50 $
So, the correct answer is “Option A”.

Note: Here, we are asked to find the compound interest for the third year and not for the first three years. Therefore, instead of finding the compound interest directly, we have taken the difference of final amounts of third and the second year. This way, we can determine the required answer.