Find the amount and compound interest on ₹ 1,25,000 for $1\dfrac{1}{2}$ years at 12% per annum, compounded half yearly.

Given,

Principal (P) = ₹ 1,25,000

Time (n) = 1 $\dfrac{1}{2}$ years = 1.5 years

Rate (r) = 12% 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 :

$\Rightarrow A = 125000 \times \Big(1 + \dfrac{12}{2 \times 100}\Big)^{1.5 \times 2} \\[1em] \Rightarrow A = 125000 \times \Big(1 + \dfrac{3}{50}\Big)^3 \\[1em] \Rightarrow A = 125000 \times \Big(\dfrac{50 + 3}{50}\Big)^3 \\[1em] \Rightarrow A = 125000 \times \Big(\dfrac{53}{50}\Big)^3 \\[1em] \Rightarrow A = 125000 \times \Big(\dfrac{148877}{125000}\Big) \\[1em] \Rightarrow A = \dfrac{125000 \times 148877}{125000} = ₹ 1,48,877$

Compound interest = Amount - Principal

= ₹ 1,48,877 - ₹ 1,25,000 = ₹ 23,877

Hence, amount = ₹ 1,48,877 and compound interest = ₹ 23,877.