At what rate of interest per annum will the present value of a perpetuity of Rs. 600 payable at the end of each quarter be Rs. 48,000 ?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5%
For a perpetuity, the present value is the payment divided by the rate per period. The payment is quarterly, so the rate found is per quarter:
\( \displaystyle 48{,}000=\frac{600}{i} \)
\( \displaystyle i=\frac{600}{48{,}000}=0.0125 \)
That is 1.25% per quarter. There are 4 quarters in a year, so the rate per annum is \( 4\times 1.25\%=5\% \).
Tip: The value 1.25% (Option 3) is the rate per quarter; the question asks for the rate per annum.