Question

Rs. $12000$ is invested for $1\frac{1}{2}$ years at compound interest annually. If Rs. $15972$ is received of at the end, then $R=$ ?

Answer 1

Principal, $P=Rs.12000$

Time, $t=1.5$ years

Rate of interest, $r=?$

Amount received after $1.5$ years $A=Rs.15972$

For compound interest,

$A=P{(1+\frac{r}{100})}^t$

$15972=12000{(1+\frac{r}{100})}^{\frac{3}{2}}$

$\frac{15972}{12000}={(1+\frac{r}{100})}^{\frac{3}{2}}$

$\frac{1331}{1000}={(1+\frac{r}{100})}^{\frac{3}{2}}$

$1+\frac{r}{100}={\left(\frac{1331}{1000}\right)}^{\frac{2}{3}}$

$1+\frac{r}{100}={\left({\left(\frac{11}{10}\right)}^3\right)}^{\frac{2}{3}}$

$1+\frac{r}{100}={\left(\frac{11}{10}\right)}^2$

$1+\frac{r}{100}=\frac{121}{100}$

$\frac{r}{100}=\frac{121}{100}-1=\frac{21}{100}$

$\Rightarrow r=21$% per annum