Find the amount and the compound interest on ₹ 10,000 in 3 years, if the rates of interest for the successive years are 10%, 15% and 20% respectively.

Given:

P = ₹ 10,000

T = 3 years

R₁ = 10%

R₂ = 15%

R₃ = 20%

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] = 10,000\Big[1 + \dfrac{10}{100}\Big]\Big[1 + \dfrac{15}{100}\Big]\Big[1 + \dfrac{20}{100}\Big]\\[1em] = 10,000\Big[1 + \dfrac{1}{10}\Big]\Big[1 + \dfrac{3}{20}\Big]\Big[1 + \dfrac{1}{5}\Big]\\[1em] = 10,000\Big[\dfrac{10}{10} + \dfrac{1}{10}\Big]\Big[\dfrac{20}{20} + \dfrac{3}{20}\Big]\Big[\dfrac{5}{5} + \dfrac{1}{5}\Big]\\[1em] = 10,000\Big[\dfrac{(10 + 1)}{10}\Big]\Big[\dfrac{(20 + 3)}{20}\Big]\Big[\dfrac{(5 + 1)}{5}\Big]\\[1em] = 10,000\Big[\dfrac{11}{10}\Big]\Big[\dfrac{23}{20}\Big]\Big[\dfrac{6}{5}\Big]\\[1em] = \Big[\dfrac{1,51,80,000}{1000}\Big]\\[1em] = 15,180

$\text{C.I. = A - P}\\[1em] = ₹ 15,180 - ₹ 10,000\\[1em] = ₹ 5,180$

Hence, the amount = ₹ 15,180 and the compound interest = ₹ 5,180.