A sum of money lent at compound interest for 2 years at 20% per annum would fetch Rs. 482 more, if the interest was payable half yearly than if it was payable annually. The sum is

case 1 : When amount is lent annually

=> $$C.I. = P[(1 + \frac{R}{100})^T - 1]$$

= $$P[1 + \frac{20}{100})^2 - 1]$$

= $$P(\frac{36}{25} - 1)$$

= $$\frac{11}{25}P$$ --------------Eqn(1)

case 2 : When amount is lent half yearly

=> $$C.I. = P[(1 + \frac{10}{100})^4 - 1]$$

= $$P[(\frac{11}{10})^4 - 1]$$

= $$\frac{4641}{10000}P$$ ----------------Eqn(2)

Subtracting eqn (1) from (2), we get :

=> $$\frac{4641}{10000}P - \frac{11}{25}P = 482$$

=> $$241P = 4820000$$

=> $$P = Rs. 20,000$$