Find the amount and the compound interest on ₹ 32,000 for 1 year at 20% per annum compounded half-yearly.

Given:

P = ₹ 32,000

R = 20%

n = 1 year

Since, interest is compounded half-yearly,

$\text{A} = P\Big[1 + \dfrac{R}{2 \times 100}\Big]^{n \times 2}\\[1em] = 32,000\Big[1 + \dfrac{20}{200}\Big]^{2\times 1}\\[1em] = 32,000\Big[1 + \dfrac{1}{10}\Big]^2\\[1em] = 32,000\Big[\dfrac{10}{10} + \dfrac{1}{10}\Big]^2\\[1em] = 32,000\Big[\dfrac{(10 + 1)}{10}\Big]^2\\[1em] = 32,000\Big[\dfrac{11}{10}\Big]^2\\[1em] = 32,000\Big[\dfrac{121}{100}\Big]\\[1em] = \Big[\dfrac{38,72,000}{100}\Big]\\[1em] = 38,720$

Also

$\text{Compound Interest = Final amount - Original Principal}\\[1em] = ₹ 38,720 - ₹ 32,000\\[1em] = ₹ 6,720$

Hence, amount = ₹ 38,720 and compound interest = ₹ 6,720.