At what rate of interest per annum will the present value of a perpetuity of Rs. 500 payable at the end of every 6 months be Rs. 10,000?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10%
The present value of a perpetuity of R per period at the rate i per period is
\( \displaystyle P=\frac{R}{i} \)
Here the payment period is 6 months, so i is the rate per half-year.
\( \displaystyle 10000=\frac{500}{i} \)
\( \displaystyle i=\frac{500}{10000} \)
\( i=0.05=5\%\ \text{per half-year} \)
The rate per annum (compounded half-yearly) is
\( 2\times 5\%=10\% \)
CBSE Applied Mathematics (Class XII):
Perpetuity
