At what rate percent per annum compound interest will ₹ 5,000 amount to ₹ 5,832 in 2 years?

Given:

P = ₹ 5,000

n = 2 years

A = ₹ 5,832

Let the rate be $r$.

As we know,

$\text{A} = P\Big[1 + \dfrac{r}{100}\Big]^n\\[1em] \Rightarrow 5,832 = 5,000\Big[1 + \dfrac{r}{100}\Big]^2\\[1em] \Rightarrow \dfrac{5,832}{5000} = \Big[1 + \dfrac{r}{100}\Big]^2\\[1em] \Rightarrow \dfrac{729}{625} = \Big[1 + \dfrac{r}{100}\Big]^2\\[1em] \Rightarrow \sqrt{\dfrac{729}{625}} = \Big[1 + \dfrac{r}{100}\Big]\\[1em] \Rightarrow 1 + \dfrac{r}{100} = \dfrac{27}{25}\\[1em] \Rightarrow \dfrac{r}{100} = \dfrac{27}{25} - 1\\[1em] \Rightarrow \dfrac{r}{100} = \dfrac{27}{25} - \dfrac{25}{25}\\[1em] \Rightarrow \dfrac{r}{100} = \dfrac{(27 - 25)}{25}\\[1em] \Rightarrow \dfrac{r}{100} = \dfrac{2}{25}\\[1em] \Rightarrow r = \dfrac{2 \times 100}{25}\\[1em] \Rightarrow r = \dfrac{200}{25}\\[1em] \Rightarrow r = 8$

Hence, the rate of interest = $8\%$.