Answer : Option A

Explanation :

Amount after 1¹â„₂ years when interest is compounded yearly
$MF#%= 5000 \times \left(1 + \dfrac{4}{100}\right)^1\times \left(1 + \dfrac{\dfrac{1}{2} \times 4}{100}\right)
= 5000 \times \dfrac{104}{100} \times \left(1 + \dfrac{2}{100}\right) \\\\ = 5000 \times \dfrac{104}{100} \times \dfrac{102}{100} = 50 \times 104 \times \dfrac{51}{50} \\\\ = 104 \times 51 = \text{Rs. }5304$MF#%
Compound Interest for 1 ¹â„₂ years when interest is compounded yearly
= Rs.(5304 - 5000)
Amount after 1¹â„₂ years when interest is compounded half-yearly
$MF#%= \text{P}\left(1 + \dfrac{\text{(R/2)}}{100}\right)^\text{2T} = 5000\left(1 + \dfrac{(4/2)}{100}\right)^{2 \times \frac{3}{2}} = 5000\left(1 + \dfrac{2}{100}\right)^3\\\\ = 5000\left(\dfrac{102}{100}\right)^3 = 5000\left(\dfrac{102}{100}\right)\left(\dfrac{102}{100}\right)\left(\dfrac{102}{100}\right) = 50 \times 102 \times \dfrac{51}{50}\times \dfrac{51}{50} \\\\ = 102 \times 51 \times \dfrac{51}{50} = 51 \times 51 \times \dfrac{51}{25} = \text{Rs. } 5306.04$MF#%
Compound Interest for 1 ¹â„₂ years when interest is compounded half-yearly
= Rs.(5306.04 - 5000)
Difference in the compound interests = (5306.04 - 5000) - (5304 - 5000) = 5306.04 - 5304 = Rs. 2.04