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. 20000?

10%

The correct answer is Option (1) → 10%

Given:

Perpetuity payment: R = 1000 (every six months)

Present value: PV = 20000

Rate per period: r

Present value of perpetuity formula: PV = $\frac{R}{r}$

Substitute the values:

20000 = $\frac{1000}{r}$

r = $\frac{1000}{20000} = 0.05$

Since the payment is every six months, the semi-annual interest rate is 5%

Annual interest rate = 2 × 5% = 10%