At what rate percent per annum will a sum of Rs 4000

Let the rate percent be $\mathrm{R}$.

We know that:

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

$410=4,000\left(1+\frac{\mathrm{R}}{100}\right)^{2}-4,000$

$4,410=4,000\left(1+\frac{\mathrm{R}}{100}\right)^{2}$

$\left(1+\frac{\mathrm{R}}{100}\right)^{2}=\frac{4,410}{4,000}$

$\left(1+\frac{\mathrm{R}}{100}\right)^{2}=1.1025$

$\left(1+\frac{\mathrm{R}}{100}\right)^{2}=(1.05)^{2}$

$1+\frac{\mathrm{R}}{100}=1.05$

$\frac{\mathrm{R}}{100}=0.05$

$\mathrm{R}=5$

Thus, the required rate percent is 5 .