The present value of a perpetual income of ₹x payable at the end of each 6 months is ₹1,80,000. If the money is worth 5% compounded semi-annually, then the value of x is ₹:

4500

The correct answer is Option (1) - 4500

$\text{Present value of perpetuity} = \frac{\text{Payment}}{i}$

$i = \frac{5\%}{2} = 2.5\% = 0.025$

$180000 = \frac{x}{0.025}$

$x = 180000 \times 0.025$

$= 4500$

The value of $x$ is ₹4500.