In what time will ₹ 1500 yield ₹ 496.50 as compound interest at 20% per year compounded half-yearly ?

Given,

C.I. = ₹ 496.50

P = ₹ 1500

Rate = 20%

A = P + C.I. = ₹ 1500 + ₹ 496.50 = ₹ 1996.50

Let time required be n years.

When interest is compounded half-yearly.

$\Rightarrow A = P\Big(1 + \dfrac{r}{2 \times 100}\Big)^{n \times 2} \\[1em] \Rightarrow 1996.50 = 1500 \times \Big(1 + \dfrac{20}{200}\Big)^{2n} \\[1em] \Rightarrow \dfrac{1996.50}{1500} = \Big(1 + \dfrac{20}{200}\Big)^{2n} \\[1em] \Rightarrow \dfrac{199650}{150000} = \Big(\dfrac{220}{200}\Big)^{2n} \\[1em] \Rightarrow \dfrac{1331}{1000} = \Big(\dfrac{11}{10}\Big)^{2n} \\[1em] \Rightarrow \Big(\dfrac{11}{10}\Big)^3 = \Big(\dfrac{11}{10}\Big)^{2n} \\[1em] \Rightarrow 2n = 3 \\[1em] \Rightarrow n = \dfrac{3}{2}.$

Hence, required time = $1\dfrac{1}{2}$ years.