On what sum of money will the difference between simple interest and compound interest for 2 years at 5% per annum be equal to ₹ 50 ?

Let P be the sum of money.

R = 5 %, T = 2 years

$\text{S.I.} = \dfrac{P \times R \times T}{100}\\[1em] = \dfrac{P \times 5 \times 2}{100}\\[1em] = \dfrac{10P}{100}\\[1em] = \dfrac{P}{10} = 0.1P$

C.I. = P $\Big(1 + \dfrac{R}{100}\Big)^n$ - P

= P x $\Big(1 + \dfrac{5}{100}\Big)^2$ - P

= P x $\Big(1 + 0.05\Big)^2$ - P

= P x $(1.05)^2$ - P

= 1.1025P - P

= 0.1025P

The difference between S.I. and C.I. = C.I. - S.I. = 50

⇒ 50 = 0.1025P - 0.1P

⇒ 50 = 0.0025P

⇒ P = $\dfrac{50}{0.0025}$

⇒ P = $\dfrac{5,00,000}{25}$

⇒ P = 20,000

Hence, the sum of money = ₹ 20,000.