Question

Nikita invests $\text{Rs.}6000$ for two years at a certain rate of interest compounded annually. At the end of the first year, it amounts to $\text{Rs.}6720$.
Calculate :
(a) The rate of interest.
(b) The amount at the end of the second year.

Answer 1

Let the rate of interest is equal to $r$ per annum.

a). For one year,

$P=\text{Rs.}6000$

$A=\text{Rs.}6720$

$n=1\text{years}$

Now, we will substitute the given values in the formula to calculate amount,

$\begin{array}{cc}A& =P{\left(1+\frac{r}{100}\right)}^n\\ 6720& =6000{\left(1+\frac{r}{100}\right)}^1\\ \frac{672}{600}& =1+\frac{r}{100}\\ \frac{r}{100}& =\frac{72}{600}\\ r& =12\end{array}$

Hence the rate of interest is equal to $12\%$.

b). Amount at the end of the second year will be,

$\begin{array}{cc}A& =P{\left(1+\frac{r}{100}\right)}^n\\ & =6000{\left(1+\frac{12}{100}\right)}^2\\ & =6000{\left(\frac{28}{25}\right)}^2\\ & =7526.4\end{array}$

Hence the amount at the end of the second year will be $\text{Rs.}7526.4$.