₹16000 invested at 10% p.a., compounded semi-annually, amounts to ₹18522. Find the time period of investment.

Rate = 10% p.a. i.e. $\dfrac{10\%}{2}$ = 5% compounded semi-annually.

Let time be n half-years.

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

Substituting values we get,

$\Rightarrow 18522 = 16000\Big(1 + \dfrac{5}{100}\Big)^n \\[1em] \Rightarrow 18522 = 16000\Big(\dfrac{105}{100}\Big)^n \\[1em] \Rightarrow \dfrac{18522}{16000} = \Big(\dfrac{21}{20}\Big)^n \\[1em] \Rightarrow \dfrac{9261}{8000} = \Big(\dfrac{21}{20}\Big)^n \\[1em] \Rightarrow \Big(\dfrac{21}{20}\Big)^3 = \Big(\dfrac{21}{20}\Big)^n \\[1em] \Rightarrow n = 3 \text{ half-years}.$

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

Hence, time = $1\dfrac{1}{2}$ years.