A sum of ₹1,00,000 invested at r% compounded half yearly will provide payments of ₹500 at the end of every 6 months. Then the value of r is:

1

The correct answer is Option (2) → 1

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

$100000 = \frac{500}{i}$

$i = \frac{500}{100000} = 0.005 = 0.5\% \text{ per half-year}$

$\text{Annual nominal rate} = 2 \times 0.5\% = 1\%$

The value of $r$ is $1\%$.