The rate of interest (per annum), at which the present value of a perpetuity of Rs. 5,000 payable at the end of every 6 months will be Rs. 40,000 is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 25%
For a perpetuity of R per period at rate i per period, the present value is
\( \displaystyle PV = \frac{R}{i} \)
Here a period is 6 months:
\( \displaystyle 40000 = \frac{5000}{i} \)
\( \displaystyle i = \frac{5000}{40000} = 0.125 = 12.5\% \text{ per half-year} \)
The rate per annum is quoted as the nominal rate compounded half-yearly, which is twice the half-yearly rate:
\(2\times 12.5\% = 25\%\) per annum
CBSE Applied Mathematics (Class XII):
Perpetuity
