At what rate per cent per annum will Rs 640 amount to Rs 774.40 in 2 years

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

$A=774.40$

$P=640$

$\mathrm{n}=2$ years

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

$\Rightarrow 774.40=640\left(1+\frac{R}{100}\right)^{2}$

$\Rightarrow \frac{774.40}{640}=\left(1+\frac{R}{100}\right)^{2}$

$\Rightarrow 1.21=\left(1+\frac{R}{100}\right)^{2}$

$\Rightarrow(1.1)^{2}=\left(1+\frac{R}{100}\right)^{2}$

$\Rightarrow 1.1-1=\frac{R}{100}$

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

$\Rightarrow R=(0.1 \times 100)=10$

Hence, the required rate is $10 \%$ p. a.