Find the rate percent per annum,

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

Because interest is compounded every six months, n will be 3 for $1.5$ years.

Now,

$\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{200}\right)^{\mathrm{n}}$

$2,315.25=2,000\left(1+\frac{\mathrm{R}}{200}\right)^{3}$

$\left(1+\frac{\mathrm{R}}{200}\right)^{3}=\frac{2,315.25}{2,000}$

$\left(1+\frac{\mathrm{R}}{200}\right)^{3}=1.157625$

$\left(1+\frac{\mathrm{R}}{200}\right)^{3}=(1.05)^{3}$

$1+\frac{\mathrm{R}}{200}=1.05$

$\frac{\mathrm{R}}{200}=0.05$

$=10$

Thus, the required rate is $10 \%$ per annum.