Question

If the present value of a perpetuity of ₹600 payable at the end of every six months is ₹18000, then the rate of interest is:

• A. \(\frac{20}{3} %\) % per annum
• B. \(\frac{22}{3} %\) % per annum
• C. \(\frac{17}{3} %\) % per annum
• D. \(\frac{10}{3} %\) % per annum

Answer 1

The Correct Option is A

To determine the rate of interest for a perpetuity, we use the formula for the present value of a perpetuity, which is given by:
\( PV = \frac{C}{r} \)where \( PV \) is the present value, \( C \) is the cash flow per period, and \( r \) is the interest rate per period.
Given:
\( PV = ₹18000 \)
\( C = ₹600 \)Substituting these values into the formula gives:
\( 18000 = \frac{600}{r} \)To find \( r \), solve the equation:
\( r = \frac{600}{18000} \)
\( r = \frac{1}{30} \)This \( r \) is the semi-annual rate of interest because payments are made every six months.
To find the annual rate, multiply by 2:
\( r_{annual} = 2 \times \frac{1}{30} \)
\( r_{annual} = \frac{2}{30} \)
\( r_{annual} \approx \frac{1}{15} \)Convert the fraction to percentage:
\( r_{annual} = \frac{1}{15} \times 100\% \)
\( r_{annual} \approx \frac{100}{15} \)%
\( r_{annual} \approx \frac{20}{3} \)%Thus, the rate of interest is \( \frac{20}{3} \)% per annum.