Let P is the principal and interest compounded half yearly at the rate of $ 20 \% $ per annum then amount after two years will be

Given:

Principal $=P$

Time $T=2\ years$

Rate of interest $R=20 \%$

To do:

We have to find the amount after 2 years.

 Solution:

Time $= 2$ years

Rate of interest $=20 \%$ per annum compounded half-yearly

$r=\frac{R}{100}$

$r=\frac{20}{100}$

$r=0.2$ per year

Amount $= P(1+\frac{r}{n})^{nT} $

$= P(1+\frac{0.2}{2})^{2 \times 2}$

$= P(1.1)^4$

$= P(1.1)^4 $

$=1.4641P$ 

Amount after 2 years $=1.4641P$.