At what rate converted semi-annually will the present value of a perpetuity of ₹750 payable at the end of every 6 months be ₹50,000 ?
Answer & explanation
Correct answer: option 1
Present value of perpetuity $=50000$.
Payment every $6$ months $=750$.
Let rate per half-year $=i$.
For a perpetuity:
$\text{PV}=\frac{\text{payment}}{i}$
$50000=\frac{750}{i}$
$i=\frac{750}{50000}=0.015$
Rate per half-year $=1.5\%$.
Nominal rate converted semi-annually:
$=2\times1.5\%=3\%$ per annum.
final answer: $3\%$ per annum convertible semi-annually