At what rate of interest will the present value of a perpetuity of Rs. 1000 payable at the end of every six months be Rs. 40000?

5%

The correct answer is Option (2) → 5%

Present Value of perpetuity is given by:

$PV = \frac{A}{r}$

where $A$ = payment per period, $r$ = interest rate per period.

Here, $PV = 40000$, $A = 1000$ (every six months).

$40000 = \frac{1000}{r}$

$r = \frac{1000}{40000} = \frac{1}{40} = 0.025$

This is the half-yearly interest rate = $2.5\%$.

Annual effective rate = $2 \times 2.5\% = 5\%$.

Required rate of interest = 5% per annum.