On what sum will the compound interest at 5% per annum for 2 years

Let the sum be Rs $\mathrm{x}$.

We know that:

$\mathrm{CI}=\mathrm{A}-\mathrm{P}$

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

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

$164=\mathrm{x}\left[\left(1+\frac{5}{100}\right)^{2}-1\right]$

$164=\mathrm{x}\left[(1.05)^{2}-1\right]$

$\mathrm{x}=\frac{164}{0.1025}$

$=1,600$

Thus, the required sum is Rs 1,600 .