Question

Ajit borrowed $Rs.2,00,000$ from a credit card company at $20\%$ per annum compounded quarterly. Find the compound interest and the amount after one year.

Answer 1

Given:-

$P=2,00,000$

$R=20\%$ but the interest is compounded quarterly so,

$R^{\prime }=\frac{20}{4}\%$

$=5\%$

$n=1$ year but as we are calculating quarterly so,

$n^{\prime }=4\times n$

$=4$

Now, by using the formula for compound interest,

$\begin{array}{cc}A& =P{\left(1+\frac{r}{100}\right)}^n\\ & =P{\left(1+\frac{R^{\prime }}{100}\right)}^{n^{\prime }}\\ & =2,00,000{\left(1+\frac{5}{100}\right)}^4\\ & =2,00,000{\left(1.05\right)}^4\\ & =2,00,000\times 1.2155\\ & =Rs.2,43,100\end{array}$

Hence, the amount after $1$ year is equal to $Rs.2,43,100.$

As we know that amount is equal to the sum of principal and inteerst. Hence,

$\begin{array}{cc}A& =I+P\\ I& =A-P\\ & =243100-200000\\ & =Rs.43,100\end{array}$

Hence, interest after $1$ year is equal to $Rs.43,100.$