Question

Find the compound interest on Rs.32000 for 9 month at 10% p.a., if the interest is being compounded quarterly.

Answer 1

Hint: Sum of money compounded quarterly is given by the formula \[A = P{\left( {1 + \dfrac{{\left( {\dfrac{R}{4}} \right)}}{{100}}} \right)^{4n}}\] , where \[P\] is the principal amount on which interest is to be calculated, \[R\] is the rate at which the amount is being compounded and \[n\] is the time for which the amount is compounded for.
In this question we are given with the principal amount, the rate of interest and the time period so by using the above formula we will find the amount after 9 months by which compound interest will be calculated.

Complete step-by-step answer:
Given
The principle amount which is being compounded \[P = Rs.32000\]
The rate at which amount is compounded \[R = 10\% \]
The time period \[n = 9months = \dfrac{9}{{12}}year = \dfrac{3}{4}year\]
Now as we know when a sum of money is compounded quarterly it’s amount is given by the formula \[A = P{\left( {1 + \dfrac{{\left( {\dfrac{R}{4}} \right)}}{{100}}} \right)^{4n}}\]
Hence, by substituting the values we can write
 \[A = \left( {3200} \right){\left( {1 + \dfrac{{\left( {\dfrac{{10}}{4}} \right)}}{{100}}} \right)^{4 \times \dfrac{3}{4}}}\]
By solving the equation, we get
 \[
  A = \left( {3200} \right){\left( {1 + \dfrac{{\left( {\dfrac{{10}}{4}} \right)}}{{100}}} \right)^{4 \times \dfrac{3}{4}}} \\
   = \left( {3200} \right){\left( {1 + \dfrac{1}{{40}}} \right)^3} \\
   = \left( {3200} \right){\left( {\dfrac{{41}}{{40}}} \right)^3} \\
   = \left( {3200} \right)\left( {\dfrac{{41}}{{40}}} \right)\left( {\dfrac{{41}}{{40}}} \right)\left( {\dfrac{{41}}{{40}}} \right) \\
   = Rs.34460.50 \;
 \]
So the amount after 9 months when principal amount was compounded quarterly will be \[ = Rs.34460.50\]
Now we know the compound interest is given by the formula \[C.I = Amount - Principle \] , hence by substituting the values we get
 \[
  C.I = 34460.50 - 32000 \\
   = Rs.2460.50 \;
 \]
Therefore, the compound interest on Rs.32000 for 9 month at 10% p.a. which is compounded quarterly \[ = Rs.2460.50\]
So, the correct answer is “Rs.2460.50”.

Note: Compound interest is the method of interest calculation on a principle amount for fixed rate and the time. It can be used to determine the time after which a sum of money can be doubled or tripled. It is also used to determine the rate of interest which is required to double or triple the money for a certain time period.