The present value (in Rs.) of a perpetuity of Rs. 3600 payable at the end of each quarter, if the interest rate is 9% per annum compounded quarterly, is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 1,60,000
The present value of a perpetuity of R paid at the end of each period is R divided by the interest rate i per period:
\( \displaystyle PV = \frac{R}{i} \)
The payments are quarterly, so the rate per quarter is
\( \displaystyle i = \frac{9\%}{4} = 2.25\% = 0.0225 \)
Then
\( \displaystyle PV = \frac{3600}{0.0225} = 1{,}60{,}000 \)
So the present value is Rs. 1,60,000.
CBSE Applied Mathematics (Class XII):
Perpetuity
