Question

Find the compound interest on Rs. $1000$ at the rate of $10$% per annum for $18$ months when interest is compounded half-yearly.

Answer 1

Here, $P=$ $1000$, $r=10$% per annum
and $n=18$ months $=\frac{18}{12}$ years $=\frac{3}{2}$ years $=1\frac{1}{2}$ years
$\therefore$ Amount after $18$ months $=P{[1+\frac{1}{2}\left(\frac{r}{100}\right)]}^{2n}$
$=1000{[1+\frac{1}{2}\left(\frac{10}{100}\right)]}^{2\times \frac{3}{2}}$
$=1000{(1+\frac{10}{200})}^3$
$=1000{\left(\frac{21}{20}\right)}^3$
$=1000\times \frac{21}{20}\times \frac{21}{20}\times \frac{21}{20}$
$=$ $1157.625$
$=$ $1157.63$
C.I. $=A-P$
$=1157.63-1000=$ $157.63$