Question

The rate of interest (per annum), at which the present value of a perpetuity of ₹5,000 payable at the end of every 6 months will be ₹40,000 is:

• A. 20%
• B. 25%
• C. 15%
• D. 30%

Answer 1

The Correct Option is B

The formula for the present value (PV) of a perpetuity is given by:

PV = \(\frac{C}{r}\),

where C is the periodic payment and r is the interest rate per period. Here, PV = 40,000 and C = 5,000.

Substituting these values:

40,000 = \(\frac{5,000}{r}\).

Simplify to find r:

r = \(\frac{5,000}{40,000}\) = 0.125 (per 6 months).

Since r = 0.125 is the rate for 6 months, the annual rate is:

r_annual = 0.125 × 2 = 0.25 = 25%.

Thus, the correct answer is 25%.