At what rate converted semi-annually will the present value of perpetuity of Rs. 750/- payable at the end of each 6 months be Rs. 25000? (where p.a. denotes per annum)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6% p.a.
For an immediate perpetuity of R per period at rate i per period, the present value is \( P=\frac{R}{i} \). Here the period is 6 months:
\( \displaystyle 25000=\frac{750}{i} \)
\( \displaystyle i=\frac{750}{25000}=0.03\text{ per half-year} \)
The nominal annual rate converted semi-annually is twice the half-yearly rate:
\( r=2\times 3\%=6\%\text{ p.a.} \)
CBSE Applied Mathematics (Class XII):
Perpetuity
