Question

The present value of a perpetual income of x paybale at the end of each 6 months is ₹ 1,80,000. If the money is worth 5% compounded semi-annually, then the value of x is ₹:

• A. 4500
• B. 7500
• C. 9000
• D. 4250

Answer 1

The Correct Option is A

To determine the value of x, we need to use the formula for the present value (PV) of a perpetuity, which is given by:

PV = \(\frac{x}{r}\)

where x is the payment per period, and r is the interest rate per period. Here, the interest rate is 5% compounded semi-annually, so the semi-annual interest rate is:

r = \(\frac{5}{100 \times 2}\) = 0.025

We are given that the present value of the perpetuity is ₹1,80,000. Substituting the given values into the formula:

1,80,000 = \(\frac{x}{0.025}\)

Solving for x:

x = 1,80,000 \(\times\) 0.025

x = ₹4,500

Thus, the value of x is ₹4,500.