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What is the difference between the compound interests on Rs. 5000 for 1  \(\frac{1}{2}\) years at 4% per annum compounded yearly and half-yearly?

Options:
A .  Rs. 2.04
B .  Rs. 3.06
C .  Rs. 4.80
D .  Rs. 8.30
Answer: Option A

C.I. when interest compounded yearly  = Rs. \(\left[5000\times\left(1+\frac{4}{100}\right)\times\left(1+\frac{\frac{1}{2}\times4}{100}\right)\right]\)


= Rs. \(\left(5000\times\frac{26}{25}\times\frac{51}{50}\right)\)


= Rs 5304.


C.I. when interest compounded half- yearly = Rs. \(\left[5000\times\left(1+\frac{2}{100}\right)^{3}\right]\)


= Rs \(\left(5000\times\frac{51}{50}\times\frac{51}{50}\times\frac{51}{50}\right)\)


= Rs. 5306.4


 So, Difference = Rs. (5306.04 - 5304) = Rs. 2.04


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