Calculate the compound interest on ₹ 5,000 in 2 years, if the rates of interest for successive years are 10% and 12% respectively.

Given:

P = ₹ 5,000

T = 2 years

R₁ = 10%

R₂ = 12%

As we know,

$\text{A} = P\Big[1 + \dfrac{R$1}{100}\Big]\Big[1 + \dfrac{R2}{100}\Big]\\[1em] = 5,000\Big[1 + \dfrac{10}{100}\Big]\Big[1 + \dfrac{12}{100}\Big]\\[1em] = 5,000\Big[1 + \dfrac{1}{10}\Big]\Big[1 + \dfrac{3}{25}\Big]\\[1em] = 5,000\Big[\dfrac{10}{10} + \dfrac{1}{10}\Big]\Big[\dfrac{25}{25} + \dfrac{3}{25}\Big]\\[1em] = 5,000\Big[\dfrac{(10 + 1)}{10}\Big]\Big[\dfrac{(25 + 3)}{25}\Big]\\[1em] = 5,000\Big[\dfrac{11}{10}\Big]\Big[\dfrac{28}{25}\Big]\\[1em] = \Big[\dfrac{15,40,000}{250}\Big]\\[1em] = ₹ 6,160

$\text{C.I. = A - P}\\[1em] = ₹ 6,160 - ₹ 5,000\\[1em] = ₹ 1,160$

Hence, compound interest = ₹ 1,160