Find the amount and the compound interest on ₹ 4,000 in 2 years, if the rate of interest for first year is 10% and for the second year is 15%.

Given:

P = ₹ 4,000

T = 2 years

R₁ = 10%

R₂ = 15%

As we know, $\text{A} = P\Big[1 + \dfrac{R$1}{100}\Big]\Big[1 + \dfrac{R2}{100}\Big]\\[1em] = 4,000\Big[1 + \dfrac{10}{100}\Big]\Big[1 + \dfrac{15}{100}\Big]\\[1em] = 4,000\Big[1 + \dfrac{1}{10}\Big]\Big[1 + \dfrac{3}{20}\Big]\\[1em] = 4,000\Big[\dfrac{10}{10} + \dfrac{1}{10}\Big]\Big[\dfrac{20}{20} + \dfrac{3}{20}\Big]\\[1em] = 4,000\Big[\dfrac{(10 + 1)}{10}\Big]\Big[\dfrac{(20 + 3)}{20}\Big]\\[1em] = 4,000\Big[\dfrac{11}{10}\Big]\Big[\dfrac{23}{20}\Big]\\[1em] = \Big[\dfrac{10,12,000}{200}\Big]\\[1em] = ₹ 5,060

$\text{C.I. = A - P}\\[1em] = ₹ 5,060 - ₹ 4,000\\[1em] = ₹ 1,060$

Hence, the amount = ₹ 5,060 and the compound interest = ₹ 1,060.