If ₹40000 amounts to ₹48620.25 in 2 years, compound interest payable half-yearly, find the rate of interest per annum.

Let rate of interest per annum be r% per annum, i.e. $\dfrac{r}{2}$% half-yearly.

n = 2 years or 4 half-years.

A = $P\Big(1 + \dfrac{r}{100}\Big)^n$

Given, A = ₹48620.25 and P = ₹40000.

Putting values in formula we get,

$\Rightarrow 48620.25 = 40000\Big(1 + \dfrac{\dfrac{r}{2}}{100}\Big)^4 \\[1em] \Rightarrow \dfrac{48620.25}{40000} = \Big(1 + \dfrac{r}{200}\Big)^4 \\[1em] \Rightarrow \dfrac{4862025}{4000000} = \Big(1 + \dfrac{r}{200}\Big)^4 \\[1em] \Rightarrow \dfrac{194481}{160000} = \Big(1 + \dfrac{r}{200}\Big)^4 \\[1em] \Rightarrow \Big(\dfrac{21}{20}\Big)^4 = \Big(1 + \dfrac{r}{200}\Big)^4 \\[1em] \Rightarrow \dfrac{21}{20} = 1 + \dfrac{r}{200} \\[1em] \Rightarrow \dfrac{21}{20} - 1 = \dfrac{r}{200} \\[1em] \Rightarrow \dfrac{21 - 20}{20} = \dfrac{r}{200} \\[1em] \Rightarrow \dfrac{1}{20} = \dfrac{r}{200} \\[1em] \Rightarrow r = \dfrac{200}{20} \\[1em] \Rightarrow r = 10\%.$

Hence, rate of interest = 10% per annum.