Find the amount and the C.I. on ₹ 12,000 in one year at 10% per annum compounded half-yearly.

Given:

P = ₹ 12,000

R = 10%

n = 1 years

When the interest is compounded half-yearly:

$\text{A} = P\Big[1 + \dfrac{R}{2 \times 100}\Big]^{2\times n}\\[1em] = 12,000\Big[1 + \dfrac{10}{200}\Big]^{2\times1}\\[1em] = 12,000\Big[1 + \dfrac{1}{20}\Big]^2\\[1em] = 12,000\Big[\dfrac{20}{20} + \dfrac{1}{20}\Big]^2\\[1em] = 12,000\Big[\dfrac{(20 + 1)}{20}\Big]^2\\[1em] = 12,000\Big[\dfrac{21}{20}\Big]^2\\[1em] = 12,000\Big[\dfrac{441}{400}\Big]\\[1em] = \Big[\dfrac{52,92,000}{400}\Big]\\[1em] = 13,230$

And

$\text{C.I. = A - P}\\[1em] \Rightarrow \text{C.I.} = 13,230 - 12,000\\[1em] = 1,230$

Hence, the amount = ₹ 13,230 and the compound interest ₹ 1,230