Find the amount and compound interest on Rs. 1,00,000 compounded semi-annually for $1\frac{1}{2}$ years at the rate of 8 % p.a.

Given data :

$p=\text{Rs.}1,00,000$

$t=1.5$ years

$r=8\%=\frac{8}{100}=0.08$

The formula to find the amount is

$A=p{(1+\frac{r}{n})}^{nt}$, here $n=2$ $[\because$ interest is compounded annually$)$

$=1,00,000{(1+\frac{8}{2\times 100})}^{2\times 1.5}$

$=1,00,000{\left(\frac{208}{200}\right)}^3$

$=1,00,000\times \frac{(104{)}^3}{(100{)}^3}$

Amount $=\text{Rs.}112486.4$

Compound interest $=$ Amount $-$ Principle

$C=A-p$

$C=112486.4-100000$

$C=\text{Rs.}12486.4$