Rohit borrowed ₹ 40,000 for 2 years at 10% per annum C.I. and Manish borrowed the same sum for the same time at 10.5% per annum simple interest. Which of these two gives less interest and by how much?

For simple interest

P = ₹ 40,000

R = 10.5%

T = 2 years

$\text{Interest} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] = \Big(\dfrac{40,000 \times 10.5 \times 2}{100}\Big)\\[1em] = \Big(\dfrac{8,40,000}{100}\Big)\\[1em] = ₹ 8,400$

For compound interest

P = ₹ 40,000

R = 10%

n = 2 years

$\text{A} = P\Big[1 + \dfrac{R}{100}\Big]^n\\[1em] = 40,000\Big[1 + \dfrac{10}{100}\Big]^2\\[1em] = 40,000\Big[1 + \dfrac{1}{10}\Big]^2\\[1em] = 40,000\Big[\dfrac{10}{10} + \dfrac{1}{10}\Big]^2\\[1em] = 40,000\Big[\dfrac{(10 + 1)}{10}\Big]^2\\[1em] = 40,000\Big[\dfrac{11}{10}\Big]^2\\[1em] = 40,000\Big[\dfrac{121}{100}\Big]\\[1em] = \Big[\dfrac{48,40,000}{100}\Big]\\[1em] = ₹ 48,400$

And

$\text{C.I. = A - P}\\[1em] = ₹ (48,400 - 40,000)\\[1em] = ₹ 8,400$

∴ C.I. is equals to S.I.

Hence, Both give equal interest.