Calculate the amount and compound interest on ₹ 16,000 for 1 year at 15% per annum, compounded half yearly.

Given,

Principal (P) = ₹ 16,000

Time (n) = 1 year

Rate (r) = 15% compounded half-yearly

When rate of interest is compounded half-yearly :

By formula,

A = $P\Big(1 + \dfrac{r}{2 \times 100}\Big)^{n \times 2}$

Substituting values we get :

$\Rightarrow A = 16000 \times \Big(1 + \dfrac{15}{2 \times 100}\Big)^{1 \times 2} \\[1em] \Rightarrow A = 16000 \times \Big(\dfrac{200+15}{200}\Big)^2 \\[1em] \Rightarrow A = 16000 \times \Big(\dfrac{215}{200}\Big)^2 \\[1em] \Rightarrow A = 16000 \times \Big(\dfrac{43}{40}\Big)^2 \\[1em] \Rightarrow A = 16000 \times \Big(\dfrac{1849}{1600}\Big) \\[1em] \Rightarrow A = \dfrac{16000 \times 1849}{1600} = ₹ 18,490.$

Compound interest = Amount - Principal = ₹ 18,490 - ₹ 16,000 = ₹ 2,490

Hence, amount = ₹ 18,490 and compound interest = ₹ 2,490.