Calculate the difference between the compound interest and the simple interest on ₹ 7,500 in two years and at 8% per annum.

P = ₹ 7,500

R = 8%

T = 2 years

For simple interest

$\text{Interest} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] = \Big(\dfrac{7,500 \times 8 \times 2}{100}\Big)\\[1em] = \Big(\dfrac{1,20,000}{100}\Big)\\[1em] = ₹ 1,200$

For compound interest

$\text{A} = P\Big[1 + \dfrac{R}{100}\Big]^n\\[1em] = 7,500\Big[1 + \dfrac{8}{100}\Big]^2\\[1em] = 7,500\Big[1 + \dfrac{2}{25}\Big]^2\\[1em] = 7,500\Big[\dfrac{25}{25} + \dfrac{2}{25}\Big]^2\\[1em] = 7,500\Big[\dfrac{(25 + 2)}{25}\Big]^2\\[1em] = 7,500\Big[\dfrac{27}{25}\Big]^2\\[1em] = 7,500\Big[\dfrac{729}{625}\Big]^2\\[1em] = \Big[\dfrac{54,67,500}{625}\Big]^2\\[1em] = ₹ 8,748$

And

$\text{C.I. = A - P}\\[1em] = ₹ (8,748 - 7,500)\\[1em] = ₹ 1,248$

Difference between C.I. and S.I.

= ₹ (1,248 - 1,200)

= ₹ 48

The difference between C.I. and S.I. = ₹ 48.