The compound interest on ₹5000 at 20% per annum for $1\dfrac{1}{2}$ years compounded half-yearly is

1. ₹6655

2. ₹1655

3. ₹1500

4. ₹1565

Rate = 20% i.e. $\dfrac{20\%}{2}$ = 10% when compounded semi-annually.

n (no. of conversion periods) = 3 half-years.

C.I. = $P\Big[\Big(1 + \dfrac{r}{100}\Big)^n - 1\Big]$

Putting values in formula we get,

$C.I. = ₹5000 \times \Big[\Big(1 + \dfrac{10}{100}\Big)^3 - 1\Big] \\[1em] = ₹5000 \times \Big[\Big(\dfrac{110}{100}\Big)^3 - 1\Big] \\[1em] = ₹5000 \times \Big[\Big(\dfrac{11}{10}\Big)^3 - 1\Big] \\[1em] = ₹5000 \times \Big[\dfrac{1331}{1000} - 1\Big] \\[1em] = ₹5000 \times \dfrac{1331 - 1000}{1000} \\[1em] = ₹5000 \times \dfrac{331}{1000} \\[1em] = ₹1655.$

Hence, Option 2 is the correct option.