A sum of Rs. 40000 invested at 10% p.a. compounded half yearly amounts to Rs. 44100. Compute the time period.

We know that, Compounded amount, $(A\; = \;P{\left[ {1 + \frac{{\frac{R}{2}}}{{100}}} \right]^{2t}})$

Where, P = principal, r = % rate of interest, t = time period in years

Here, A = Rs. 44100, P = Rs. 40000, R = 10%

Since interest is compounded half yearly, i.e. twice a year, rate will become (R/2) and time period will become (2t).

$(\begin{array}{l}
44100 = 40000{\left[ {1 + \frac{{\frac{{10}}{2}}}{{100}}} \right]^{2t}}\\
\Rightarrow {\left[ {1 + \frac{1}{{20}}} \right]^{2t}} = \frac{{44100}}{{40000}}\\
\Rightarrow \;{\left[ {\frac{{21}}{{20}}} \right]^{2t}} = \frac{{441}}{{400}}\\
\Rightarrow \;{\left[ {\frac{{21}}{{20}}} \right]^{2t}} = {\left( {\frac{{21}}{{20}}} \right)^2}
\end{array})$

On comparing both sides, we get

t = 1 year.