At what rate of interest will the present value of a perpetuity of Rs. 10000 payable at the end of every six months be Rs. 200,000?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10% per annum
For a perpetuity of R per period at rate i per period, the present value is
\( \displaystyle P=\frac{R}{i} \)
The payments are half-yearly, so i is the rate per half-year:
\( \displaystyle 200{,}000=\frac{10{,}000}{i} \)
\( \displaystyle i=\frac{10{,}000}{200{,}000}=0.05 \)
That is 5% per half-year. The annual rate (compounded half-yearly) is \( 2\times 5\%=10\% \) per annum.
CBSE Applied Mathematics (Class XII):
Perpetuity
