At what rate of interest will the present value of a perpetuity of Rs. 1000 payable at the end of every six months be Rs. 20000?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 10 %
For a perpetuity of R paid at the end of each period, the present value is \(P = \frac{R}{i}\), where i is the rate per period. Here the period is six months:
\( \displaystyle 20000 = \frac{1000}{i} \)
\( \displaystyle i = \frac{1000}{20000} = 0.05 \)
So the rate is 5% per half-year. Rates of interest are quoted per annum, and 5% per half-year is the nominal rate of 2 × 5% = 10% per annum, compounded half-yearly.