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?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 5% per annum
$\text{Present value of perpetuity}=20000.$
$\text{Payment every 6 months}=500.$
$\text{For perpetuity: }PV=\frac{R}{i}.$
$20000=\frac{500}{i}.$
$i=\frac{500}{20000}=\frac{1}{40}=0.025.$
$\text{Interest per half-year}=2.5\%.$
$\text{Annual rate}=2\times2.5\%=5\%.$
$\text{Required rate of interest}=5\%\text{ per annum}.$