At what rate of interest will the present value of a perpetuity of Rs. 1000 payable at the end of every six months be Rs. 40000?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5%
For a perpetuity of R per period at rate i per period, the present value of a perpetuity is
\( \displaystyle P = \frac{R}{i} \)
The payments are made every six months, so i is the rate per half-year:
\( \displaystyle 40000 = \frac{1000}{i} \)
\( \displaystyle i = \frac{1000}{40000} = 0.025 = 2.5\% \)
A rate of 2.5% per half-year is a rate of \(2 \times 2.5\% = 5\%\) per annum, compounded half-yearly.
CBSE Applied Mathematics (Class XII):
Perpetuity
