Question

Find the compound interest on $6,000$ at the rate of $9\%$ p.a. for $18$ months when interest is compounded semi-annually.

Answer 1

Given: $Principal=6,000$

$Rate=9\%$

$=\frac{9}{100}=0.09$

and $Time=n=18$ months $=\frac{3}{2}$ years

Amount after $2$ years $=P{(1+\frac{r}{2})}^{2n}$

$=6,000{(1+\frac{0.09}{2})}^{2\times \frac{3}{2}}$

$=6000{(1+0.45)}^3$

$=6,000\times {1.45}^3$

$=18291.75$

$\therefore C.I=A-P$

$=18291.75-6000$

$=12,291.75$

$C.I=Rs.12,291.75$