Question

If principal $=Rs.100000$, rate of interest $=10\%$ compounded half-yearly. Find Amount after $6$ months.

Answer 1

From question,

Principal $\left(P\right)=Rs.100000$

Rate of interest $\left(R\right)=10\%$ compounded half-yearly

Number of times interest compounded per time period $\left(n\right)=2$

Number of time period $\left(t\right)=6$ months $=\frac{1}{2}$ year

We know that,

$\begin{array}{cc}A& =P{(1+\frac{R}{100n})}^{nt}\\ & =100000{(1+\frac{10}{200})}^{2\times \frac{1}{2}}\\ & =100000{(1+\frac{1}{20})}^1\\ & =100000\times \frac{21}{20}\\ & =5000\times 21\\ & =105000\end{array}$

Therefore, amount after $6$ months $=Rs.105,000$