Find the difference between the simple interest and compound interest on ₹2500 for 2 years at 4% per annum, compound interest being reckoned semi-annually.

Since interest is calculated half yearly, hence rate = $\dfrac{4\%}{2} = 2\%.$

Time = 2 years or 4 half-years.

S.I.= $\dfrac{P \times R \times T}{100}$.

Putting values in formula we get,

$S.I. = \dfrac{₹2500 \times 2 \times 4}{100} \\[1em] = ₹\dfrac{20000}{100} \\[1em] = ₹200.$

C.I. = $P\Big[\Big(1 + \dfrac{r}{100}\Big)^n - 1\Big]$

Putting values in formula we get,

$C.I. = P\Big[\Big(1 + \dfrac{r}{100}\Big)^n - 1\Big] \\[1em] = ₹2500 \times \Big[\Big(1 + \dfrac{2}{100}\Big)^4 - 1\Big] \\[1em] = ₹2500 \times \Big[\Big(\dfrac{102}{100}\Big)^4 - 1\Big] \\[1em] = ₹2500 \times \Big[\Big(\dfrac{51}{50}\Big)^4 - 1\Big] \\[1em] = ₹2500 \times \Big[\dfrac{6765201}{6250000} - 1\Big] \\[1em] = ₹2500 \times \Big[\dfrac{6765201 - 6250000}{6250000}\Big] \\[1em] = ₹2500 \times \Big[\dfrac{515201}{6250000}\Big] \\[1em] = ₹\dfrac{515201}{2500} \\[1em] = ₹206.084$

C.I. - S.I. = ₹206.084 - ₹200 = ₹6.084

Hence, the difference between C.I. and S.I. = ₹6.084