What is the difference between the compound interests on 5,000/- for 1 year at 4% per annum compounded yearly and half-yearly ?

C.I. compounded half yearly = $$P [(1 + \frac{R}{200})^2T - 1]$$

= $$5000 [(1 + \frac{4}{200})^2 - 1]$$

= $$5000 [(\frac{51}{50})^2 - 1]$$

= $$5000 (\frac{2601}{2500} - 1) = 5000 (\frac{101}{2500})$$

= $$101 \times 2 = 202$$

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

= $$5000 [(1 + \frac{4}{100})^1 - 1]$$

= $$5000 [(1 + \frac{1}{25}) - 1]$$

= $$5000 (\frac{26}{25} - 1) = 5000 (\frac{1}{25})$$

= $$200$$

$$\therefore$$ Required difference = 202 - 200 = Rs. 2