Calculate the compound interest on ₹ 15,000 in 3 years; if the rates of interest for successive years are 6%, 8% and 10% respectively.

Given:

P = ₹ 15,000

T = 3 years

R₁ = 6%

R₂ = 8%

R₃ = 10%

As we know,

$\text{A} = P\Big[1 + \dfrac{R$1}{100}\Big]\Big[1 + \dfrac{R2}{100}\Big]\Big[1 + \dfrac{R_3}{100}\Big]\\[1em] = 15,000\Big[1 + \dfrac{6}{100}\Big]\Big[1 + \dfrac{8}{100}\Big]\Big[1 + \dfrac{10}{100}\Big]\\[1em] = 15,000\Big[1 + \dfrac{3}{50}\Big]\Big[1 + \dfrac{2}{25}\Big]\Big[1 + \dfrac{1}{10}\Big]\\[1em] = 15,000\Big[\dfrac{50}{50} + \dfrac{3}{50}\Big]\Big[\dfrac{25}{25} + \dfrac{2}{25}\Big]\Big[\dfrac{10}{10} + \dfrac{1}{10}\Big]\\[1em] = 15,000\Big[\dfrac{(50 + 3)}{50}\Big]\Big[\dfrac{(25 + 2)}{25}\Big]\Big[\dfrac{(10 + 1)}{10}\Big]\\[1em] = 15,000\Big[\dfrac{53}{50}\Big]\Big[\dfrac{27}{25}\Big]\Big[\dfrac{11}{10}\Big]\\[1em] = \Big[\dfrac{23,61,15,000}{12500}\Big]\\[1em] = 18,889.20

$\text{C.I. = A - P}\\[1em] = ₹ 18,889.20 - ₹ 15,000\\[1em] = ₹ 3,889.20$

Hence, compound interest = ₹ 3,889.20