Sudarshan invested ₹60000 in a finance company and received ₹79860 after $1\dfrac{1}{2}$ years. Find the rate of interest per annum compounded half-yearly.

Let rate of interest be r% p.a. i.e. $\dfrac{r\%}{2}$ if compounded half-yearly.

n = $1\dfrac{1}{2}$ years or 3 half-years.

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

Substituting values in formula we get,

$\Rightarrow 79860 = 60000\Big(1 + \dfrac{r}{200}\Big)^3 \\[1em] \Rightarrow \dfrac{79860}{60000} = \Big(1 + \dfrac{r}{200}\Big)^3 \\[1em] \Rightarrow \dfrac{1331}{1000} = \Big(1 + \dfrac{r}{200}\Big)^3 \\[1em] \Rightarrow \Big(\dfrac{11}{10}\Big)^3 = \Big(1 + \dfrac{r}{200}\Big)^3 \\[1em] \Rightarrow \dfrac{11}{10} = 1 + \dfrac{r}{200} \\[1em] \Rightarrow \dfrac{11}{10} - 1 = \dfrac{r}{200} \\[1em] \Rightarrow \dfrac{1}{10} = \dfrac{r}{200} \\[1em] \Rightarrow r = \dfrac{200}{10} = 20\%.$

Hence, the rate of interest = 20% per annum.