Find the rate at which a sum of money will double itself in 3 years,

Let the rate percent per annum be $R$.

Then,

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

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

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

$\left(1+\frac{\mathrm{R}}{100}\right)=1.2599$

$\frac{\mathrm{R}}{100}=0.2599$

$\mathrm{R}=25.99$

Thus, the required rate is $25.99 \%$ per annum.