If the cash equivalent of a perpetuity of Rs. 1200 payable at the end of each quarter is Rs. 96,000, then the rate of interest convertible quarterly is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 5 %
For a perpetuity of R per period at rate i per period, the present value (cash equivalent) is \( P=\frac{R}{i} \). Here the period is a quarter:
\( \displaystyle 96000=\frac{1200}{i} \)
\( \displaystyle i=\frac{1200}{96000} \)
\( =0.0125\ \text{per quarter} \)
The annual rate convertible quarterly is 4 × 1.25% = 5%.