At what rate per cent per annum will Rs 4000 amount to Rs 4410 in 2 years

Let $R \% p . a .$ be the required rate.

$A=4410$

$P=4000$

$n=2$ years

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

$\Rightarrow 4410=4000\left(1+\frac{\mathrm{R}}{100}\right)^{2}$

$\Rightarrow \frac{4410}{4000}=\left(1+\frac{R}{100}\right)^{2}$

$\Rightarrow \frac{441}{400}=\left(1+\frac{R}{100}\right)^{2}$

$\Rightarrow\left(\frac{21}{20}\right)^{2}=\left(1+\frac{R}{100}\right)^{2}$

$\Rightarrow \frac{21}{20}-1=\frac{R}{100}$

$\Rightarrow \frac{21-20}{20}=\frac{R}{100}$

$\Rightarrow \frac{1}{20}=\frac{R}{100}$

$\Rightarrow R=\left(\frac{1 \times 100}{20}\right)=5$

Hence, the required rate is $5 \%$ p.a.