If the cash equivalent of a perpetuity of Rs. 1200 payable at the end of each quarter is Rs. 96000, then the rate of interest convertible quarterly:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 5%
The cash equivalent (present value) of a perpetuity of R paid at the end of each period, at the rate i per period, is
\( \displaystyle P = \frac{R}{i} \)
Here the period is a quarter:
\( \displaystyle 96000 = \frac{1200}{i} \)
\( \displaystyle i = \frac{1200}{96000} = 0.0125 \)
That is 1.25% per quarter. The annual rate convertible quarterly is four times the quarterly rate:
\(4 \times 1.25\% = 5\%\)