In what time will ₹2400 amount to ₹2646 at 10% p.a. compounded semi-annually?

Since, interest is compounded semi-annually, rate = $\dfrac{10\%}{2} = 5\%.$

Let time be n half-years,

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

Substituting values in formula we get,

$\Rightarrow 2646 = 2400\Big(1 + \dfrac{5}{100}\Big)^n \\[1em] \Rightarrow \dfrac{2646}{2400} = \Big(1 + \dfrac{5}{100}\Big)^n \\[1em] \Rightarrow \dfrac{2646}{2400} = \Big(\dfrac{105}{100}\Big)^n \\[1em] \Rightarrow \dfrac{441}{400} = \Big(\dfrac{21}{20}\Big)^n \\[1em] \Rightarrow \Big(\dfrac{21}{20}\Big)^2 = \Big(\dfrac{21}{20}\Big)^n \\[1em] \Rightarrow n = 2.$

Time = 2 half-years or 1 year.

Hence, in 1 year ₹2400 amounts to ₹2646 at 10% p.a. compounded semi-annually.