Find the amount and the compound interest on ₹ 20,000 for $1\dfrac{1}{2}$ years at 10% per annum compounded half-yearly.

Given:

P = ₹ 20,000

R = 10%

n = $1\dfrac{1}{2}$ years

= $\dfrac{3}{2}$ years

Since, interest is compounded half-yearly,

$\text{A} = P\Big[1 + \dfrac{R}{2 \times 100}\Big]^{n \times 2}\\[1em] = 20,000\Big[1 + \dfrac{10}{200}\Big]^{2\times \dfrac{3}{2}}\\[1em] = 20,000\Big[1 + \dfrac{1}{20}\Big]^3\\[1em] = 20,000\Big[\dfrac{20}{20} + \dfrac{1}{20}\Big]^3\\[1em] = 20,000\Big[\dfrac{(20 + 1)}{20}\Big]^3\\[1em] = 20,000\Big[\dfrac{21}{20}\Big]^3\\[1em] = 20,000\Big[\dfrac{9,261}{8,000}\Big]\\[1em] = \Big[\dfrac{18,52,20,000}{8,000}\Big]\\[1em] = 23,152.50$

Also

$\text{Compound Interest = Final amount - Original Principal}\\[1em] = ₹ 23,152.50 - ₹ 20,000\\[1em] = ₹ 3,152.50$

Hence, amount = ₹ 23,152.50 and compound interest = ₹ 3,152.50.