Question

Find the compound interest on Rs. 12500 at $ 8\% $ per annum for 9 months compounded quarterly.
A. 1020
B. 1428
C. 765
D. 550

Answer 1

Hint: To solve this question, we need to gather information from the question such as principal, rate of interest and time and then to find the compound interest put these values in the formula given as
${\text{total amount}} = {\text{principal amount}} \times {\left( {{\text{1 + }}\dfrac{{{\text{rate}}}}{{100}}} \right)^{{\text{time}}}}$

Complete step-by-step answer:
Given that
Principal amount= Rs. 12500
Rate compounded quarterly
\[ \Rightarrow {\text{rate}} = \dfrac{8}{4} = 2\% \]
Time =9 months
$ = \dfrac{9}{{12}}years = \dfrac{9}{{12}} \times 4{\text{ }}quarters = 3{\text{ }}quaters$
As we know that,
 Compound interest = total amount – principal amount
Total amount is given by
$ \Rightarrow {\text{total amount}} = {\text{principal amount}} \times {\left( {{\text{1 + }}\dfrac{{{\text{rate}}}}{{100}}} \right)^{{\text{time}}}}$
Substituting the values in the above formula, we get
\[
  \Rightarrow {\text{total amount}} = 12500 \times {\left( {1 + \dfrac{2}{{100}}} \right)^3} = 12500 \times {\left( {\dfrac{{51}}{{50}}} \right)^3} \\
   \Rightarrow {\text{total amount}} = {\text{Rs}}{\text{. 13265}} \\
\]

Compound interest = total amount – principal amount
$
   = {\text{Rs}}{\text{. }}\left( {13265 - 12500} \right) \\
   = {\text{Rs}}{\text{. 765}} \\
 $
Hence, compound interest is 765 rupees.

So, the correct answer is “Option C”.

Note: Remember the formula of total amount, when interest is compounded timely. This question is formula based and some values or conditions are given in the questions. You have to find those values from the question and put them directly into the formula. And always try to solve the problems in steps such as the first step: find the given conditions or values and Second, which formula to be used and so on.