Question

The present value (in ₹.) of a perpetuity of ₹.3600 payable at the end of each quarter, if the interest rate is 9% per annum compounded quarterly, is:

• A. ₹2,40,000
• B. ₹1,60,000
• C. ₹2,00,000
• D. ₹3,20,000

Answer 1

The Correct Option is B

To find the present value of a perpetuity payable at the end of each quarter, we need to use the formula for the present value of a perpetuity:

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

where \(PV\) is the present value, \(C\) is the cash flow per period, and \(r\) is the effective interest rate per period.

In this problem, the cash flow per period \(C\) is ₹3600, and the annual interest rate is 9%, compounded quarterly. To find the quarterly interest rate, we divide the annual rate by 4:

\(r = \frac{9\%}{4} = 2.25\%\) per quarter

Convert this percentage rate to a decimal by dividing by 100:

\(r = \frac{2.25}{100} = 0.0225\)

Substitute the values into the perpetuity formula:

PV = \(\frac{3600}{0.0225}\)

Calculate the division to find the present value:

PV = ₹160,000

Therefore, the present value of the perpetuity is ₹1,60,000.