Find the amount and the C.I. on ₹ 8,000 in $1\dfrac{1}{2}$ years at 20% per year compounded half-yearly.

Given:

P = ₹ 8,000

R = 20%

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

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

When the interest is compounded half-yearly:

$\text{A} = P\Big[1 + \dfrac{R}{2 \times 100}\Big]^{2\times n}\\[1em] = 8,000\Big[1 + \dfrac{20}{200}\Big]^{2\times\dfrac{3}{2}}\\[1em] = 8,000\Big[1 + \dfrac{1}{10}\Big]^3\\[1em] = 8,000\Big[\dfrac{10}{10} + \dfrac{1}{10}\Big]^3\\[1em] = 8,000\Big[\dfrac{(10 + 1)}{10}\Big]^3\\[1em] = 8,000\Big[\dfrac{11}{10}\Big]^3\\[1em] = 8,000\Big[\dfrac{1331}{1000}\Big]\\[1em] = \Big[\dfrac{1,06,48,000}{1000}\Big]\\[1em] = 10,648$

And

$\text{C.I. = A - P}\\[1em] \Rightarrow \text{C.I.} = 10,648 - 8,000\\[1em] = 2,648$

Hence, the amount = ₹ 10,648 and the compound interest = ₹ 2,648