At what rate of interest will the present value of a perpetuity of Rs. 600 payable at the end of every 3 months be Rs. 18,000?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 13.33%
For a perpetuity of R paid at the end of every period, the present value is \(P = \frac{R}{i}\), where i is the rate per payment period. Here the period is a quarter:
\( \displaystyle 18000 = \frac{600}{i} \)
\( \displaystyle i = \frac{600}{18000} = \frac{1}{30} \text{ per quarter} \)
The rate per annum (compounded quarterly) is 4 times the quarterly rate:
\( \displaystyle 4 \times \frac{1}{30} = \frac{2}{15} = 0.1333 \)
So the rate of interest is 13.33% per annum, compounded quarterly.
CBSE Applied Mathematics (Class XII):
Perpetuity
