Find the rate percent per annum if Rs 2000 amount to Rs 2662 in

Let the rate of interest be $\mathrm{R} \%$.

Then,

$\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}$

$2,662=2,000\left(1+\frac{\mathrm{R}}{100}\right)^{3}$

$\left(1+\frac{\mathrm{R}}{100}\right)^{3}=\frac{2,662}{2,000}$

$\left(1+\frac{\mathrm{R}}{100}\right)^{3}=1.331$

$\left(1+\frac{\mathrm{R}}{100}\right)^{3}=(1.1)^{3}$

$\left(1+\frac{\mathrm{R}}{100}\right)=1.1$

$\frac{\mathrm{R}}{100}=0.1$

$\mathrm{R}=10$

Because the interest rate is being compounded half - yearly, it is $20 \%$ per annum.