The present value of a perpetual income of Rs. R at the end of each 6 months is Rs. 92,000. The value of R if money is worth 5% compounded semi-annually is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Rs. 2300
The present value of a perpetuity of R paid at the end of every period is \( \mathrm{PV}=\frac{R}{i} \), where i is the rate per period.
The payments are half-yearly, so the rate per half-year is
\( \displaystyle i=\frac{5\%}{2}=2.5\%=0.025 \)
\( \displaystyle 92000=\frac{R}{0.025} \)
\( \displaystyle R=92000\times 0.025=2300 \)
So R = Rs. 2300.
CBSE Applied Mathematics (Class XII):
Perpetuity
