Question

Find the amount and the $C.I.$ on $Rs.8000$ in $1\frac{1}{2}$ years at $20\%$ per year compounded half-yearly.

Answer 1

Principal $\left(P\right)=Rs.8000$
Rate $=20\%$ per year
Time $=1\frac{1}{2}$ years $=\frac{3}{2}$ years

n $=$ number of times interest added in the given time i.e. $1\frac{1}{2}$ years $=3$

Rate @ half yearly, $r=\frac{20}{2}=10\%$

Amount, $A=P\times {(1+\frac{r}{100})}^n$

$=Rs.8000\times {(1+\frac{10}{100})}^3$

$=Rs.8000\times {\left(\frac{11}{10}\right)}^3$

$=Rs.8000\times \frac{11}{10}\times \frac{11}{10}\times \frac{11}{10}$

$\therefore A=Rs.10648$

Compound Interest, $C.I=Rs.10648-Rs.8000=Rs.2648.$