The present value of a perpetual income of Rs. x payable at the end of each 6 months is Rs. 1,80,000. If the money is worth 5% compounded semi-annually, then the value of x is Rs.:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4500
For a perpetuity of R paid at the end of each period, with rate i per period, the present value is
\( \displaystyle PV = \frac{R}{i} \)
The period is 6 months, so the rate per period is
\( \displaystyle i = \frac{5\%}{2} = 0.025 \)
Then
\( \displaystyle 1{,}80{,}000 = \frac{x}{0.025} \)
\(x = 1{,}80{,}000 \times 0.025 = 4500\)
CBSE Applied Mathematics (Class XII):
Perpetuity
