Question

Calculate the compounded interest on $Rs.18000$ for $1\frac{1}{2}$ years at the rate of $10\%$ p.a. compounded semi annually.

Answer 1

Given initial principal amount $P=Rs.18000$
Time $t=1\frac{1}{2}=\frac{3}{2}$ years
Rate $r=10\%$ per annum compounded semi annually.
Since, we have compound interest formula
Then, $A=P{(1+\frac{r}{n\times 100})}^{n\times t}$ .......(1)
Where, $n$ is number times the interest compound annually, since here interest compound semi annually, so $n=2$
By substitute values of $P,r$ and $n$ in above formula of equation(1), we get
$A=18000{(1+\frac{10}{2\times 100})}^{\frac{3\times 2}{2}}$
$A=18000{(1+\frac{1}{2\times 10})}^3$
$A=18000\times \frac{21}{20}\times \frac{21}{20}\times \frac{21}{20}$

$A=\frac{9\times 21\times 21\times 21}{4}$
$A=\frac{83349}{4}$

$A=Rs.20837.25$

Hence, the required amount is $Rs.20837.25$