The difference between the S.I. and C.I. on a certain sum of money for 2 years at 4% per annum is Rs 20.

Given:

$\mathrm{CI}-\mathrm{SI}=\mathrm{Rs} 20$

$\left[\mathrm{P}\left(1+\frac{4}{100}\right)^{2}-\mathrm{P}\right]-\frac{\mathrm{P} \times 4 \times 2}{100}=20$

$\mathrm{P}\left[\left(1.04^{2}-1\right)\right]-0.08 \mathrm{P}=20$

$0.0816 \mathrm{P}-0.08 \mathrm{P}=20$

$0.0016 \mathrm{P}=20$

$\mathrm{P}=\frac{20}{0.0016}$

$=12,500$

Thus, the required sum is Rs 12,500 .