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 ?

3%

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