At what rate of interest will the present value of a perpetuity of ₹500 payable at the end of every 6 months be ₹20,000?

5% per annum

The correct answer is Option (3) → 5% per annum

$\text{Present value of perpetuity}=20000.$

$\text{Payment every 6 months}=500.$

$\text{For perpetuity: }PV=\frac{R}{i}.$

$20000=\frac{500}{i}.$

$i=\frac{500}{20000}=\frac{1}{40}=0.025.$

$\text{Interest per half-year}=2.5\%.$

$\text{Annual rate}=2\times2.5\%=5\%.$

$\text{Required rate of interest}=5\%\text{ per annum}.$