The present value of an immediate perpetuity of Rs. R payable at the end of every year at the rate of i per period per rupee is given by:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \displaystyle\frac{R}{i} \)
A perpetuity pays R at the end of every period for ever. Its present value P is the sum which, invested at rate i, earns exactly R as interest each period, leaving P itself intact:
\( P\times i=R \)
\( \displaystyle P=\frac{R}{i} \)
The same result comes from the sum of the infinite geometric series of discounted payments:
\( \displaystyle P=\frac{R}{1+i}+\frac{R}{(1+i)^{2}}+\cdots \)
\( \displaystyle =\frac{\frac{R}{1+i}}{1-\frac{1}{1+i}} \)
\( \displaystyle =\frac{R}{i} \)
CBSE Applied Mathematics (Class XII):
Perpetuity
