Question

Find the compound interest on $ Rs.\,320000 $ for one year at the rate of $ 20\% $ per annum, if the interest is compounded quarterly.

Answer 1

Hint: In this question, we need to determine the compound interest. We will use the formula of the amount and substitute the values to determine the value of the amount. Then, apply the value of the amount that will be determined in the formula of the compound interest to determine the required compound interest.

Complete step-by-step answer:
We need to determine the compound interest.
We know that,
Amount $ = P{\left( {1 + \dfrac{r}{{100}}} \right)^n} $
Where $ A $ =total accrued amount
 $ P $ =principle amount
 $ r $ =rate of interest per year in decimal, $ r = \dfrac{R}{{100}} $ ( $ R $ is the rate of interest per year as a percent)
 $ n $ =time period involved in months or years
Therefore, it is given that $ P = 320000 $ , $ r = \dfrac{{20}}{{400}} $ and $ n = 4 $
Now, by applying the values, we have,
Amount $ = 320000{\left( {1 + \dfrac{{20}}{{400}}} \right)^4} $
 $ = 320000{\left( {1 + 0.05} \right)^4} $
 $ = 320000{\left( {1.05} \right)^4} $
 $ = 388962 $
We know that,
\[Compound\,interest = Amount - Principle\]
Thus, we have,
 $ = 388962 - 320000 $
 $ = 68962 $
Hence, the compound interest is $ 68962 $ .
So, the correct answer is “Rs.68962”.

Note: In this question, it is important to note here that in the question it is given that the interest is compounded quarterly, so here we have taken the $ n $ as $ 4 $ . The mistakes can occur here, that as it is given one year, some will apply $ n = 1 $ . And, also we are taking $ r = \dfrac{{20}}{{400}} $ here for the same. Here some may take $ r $ as $ \dfrac{{20}}{{100}} $ which is wrong. So, be confident about the given and read it carefully. Generally, compound interest is the addition of interest to the principle sum of a loan or deposit, or in other words interest on interest. And, the principal amount is the rate of money to be invested.