[Rs. 2.04] What is the difference between the compound interests on Rs. 5000 for 1 \dfrac{1}{2} years at 4%

For Competitive Exams

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

Rs. 2.04

Rs. 3.06

Rs. 4.80

Rs. 8.30

Explanation:

C.I. when interest is compounded half-yearly	= Rs.$ \left[5000 \times\left(1 +\dfrac{4}{100} \right)\times\left(1 +\dfrac{\dfrac{1}{2} \times 4}{100} \right)\right] $
	= Rs.$ \left(5000 \times\dfrac{26}{25} \times\dfrac{51}{50} \right) $
	= Rs. 5304.

C.I. when interest is compounded half-yearly	= Rs.$ \left[5000 \times\left(1 +\dfrac{2}{100} \right)^3\right] $
	= Rs.$ \left(5000 \times\dfrac{51}{50} \times\dfrac{51}{50} \times\dfrac{51}{50} \right) $
	= Rs. 5306.04

$\therefore$ Difference = Rs. (5306.04 - 5304) = Rs. 2.04

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