A trust invites a deposit of lump sum amount from individual so that annual scholarship of Rs.5000 is paid. Rate of interest is 5% per annum. If the scholarship is to start at the end of this year then the amount needed to deposit to Trust is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 1,00,000
A scholarship paid every year without end, starting at the end of the first year, is an ordinary perpetuity. Its present value is the payment divided by the rate:
\( \displaystyle P = \frac{R}{i} = \frac{5000}{0.05} = 100000 \)
So the deposit needed is Rs. 1,00,000. The yearly interest on it, \(5\%\) of 100000, is exactly the scholarship of Rs. 5000.
CBSE Applied Mathematics (Class XII):
Perpetuity
