Question

The compound interest on $Rs8,000$ for one year at $16\%$p.a. compounded half yearly is ______, given that${(1.08)}^2=1.1664.$

Answer 1

Compound interest:

Principal $=₹8000$

Time period $=1$ year

Rate $=16\%=\frac{16}{100}=0.16$

$\mathbf{Amount}\left(A\right)\mathbf{=}\mathbf{P}{\left(1+\frac{r}{n}\right)}^{\mathbf{nt}}$

$n=2$ (compounded half-yearly in a year)

$Amount\left(A\right)=8000\times {\left(1+\frac{0.16}{2}\right)}^{2\times 1}$

$\begin{array}{rcl}A& =& 8000{\left(1+0.08\right)}^2\\ & =& 8000{\left(1.08\right)}^2\\ & =& 8000\times 1.1664\\ & \Rightarrow & A=9331.2\end{array}$

Hence,the compound interest on $Rs8,000$ for one year at $16\%$p.a. compounded half yearly is $9331.2$