At what rate of interest will the present value of a perpetuity of Rs. 600 payable at the end of each quarter be Rs. 40,000?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 6% per annum
The present value of a perpetuity is \( P=\frac{R}{i} \), where R is the payment per period and i the rate per period.
The payments are quarterly, so i is the rate per quarter:
\( \displaystyle 40{,}000=\frac{600}{i} \)
\( \displaystyle i=\frac{600}{40{,}000}=0.015 \)
This is 1.5% per quarter, so
\( \displaystyle \text{rate per annum}=4\times 1.5\%=6\% \)
CBSE Applied Mathematics (Class XII):
Perpetuity
