The amount of money needed to ensure for a prize of Rs. 5000 at the beginning of each year indefinitely if money is worth 5% compounded annually is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs. 1,05,000
A payment made at the beginning of every year forever is a perpetuity due. The first prize is paid at once, and the later prizes form an ordinary perpetuity, whose present value is \(\frac{R}{i}\):
\( \displaystyle PV = R + \frac{R}{i} \)
With \(R = 5000\) and \(i = 0.05\):
\( \displaystyle PV = 5000 + \frac{5000}{0.05} \)
\(= 5000 + 100000 = 105000\)
So Rs. 1,05,000 is needed. (If the prize were paid at the end of each year, Rs. 1,00,000 would be enough.)
CBSE Applied Mathematics (Class XII):
Perpetuity
