The present value of a perpetuity of Rs. \( x \) at the end of every 6 months is Rs. 4,00,000. If money is worth 6% per annum compounded semi-annually, what is value of \( x \) ?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 12,000
For a perpetuity of R paid at the end of each period, the present value is
\( \displaystyle P=\frac{R}{i} \)
Payments are half-yearly, so the rate per period is \( i=\frac{6\%}{2}=0.03 \).
\( \displaystyle 400000=\frac{x}{0.03} \)
\( \displaystyle x=400000\times 0.03 \)
\( \displaystyle =12000 \)
So x = Rs. 12,000.
CBSE Applied Mathematics (Class XII):
Perpetuity
