Question

I invested Rs. $12000$ in a company at compound interest compounded half yearly. After $18$ months, I received Rs. $15972$ from the company. Find the rate of interest per annum.

Answer 1

Principal $=Rs.12000$

Amount $=Rs.15972$

Time $=18$ months $=3$ and half years

$Amount=Principal{(1+\frac{R}{100})}^n$

$\Rightarrow 15972=12000{(1+\frac{R}{100})}^3$

$\Rightarrow \frac{15972}{12000}={(1+\frac{R}{100})}^3$ $\Rightarrow \frac{1331}{1000}={(1+\frac{R}{100})}^3$

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

$\Rightarrow 1+\frac{1}{10}=1+\frac{R}{100}$

$\Rightarrow \frac{R}{100}=\frac{1}{10}$

$\Rightarrow R=\frac{1}{10}\times 100=10\%$

Rate of interest per half year $=10\%$

$\therefore$ Rate of interest per annum $=10\times 2=20\%$