The present value of a sequence of payments of Rs. 2000 made at the end of every 6 months and continuing forever, if money is worth 8% per annum compounded semi-annually, is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 50000
Payments that continue forever form a perpetuity. For a payment R at the end of each period and rate i per period,
\( \displaystyle PV = \frac{R}{i} \)
The period is 6 months, so
\( \displaystyle i = \frac{8\%}{2} = 4\% = 0.04 \)
\( \displaystyle PV = \frac{2000}{0.04} = 50000 \)
CBSE Applied Mathematics (Class XII):
Perpetuity
