The present value of a perpetual income of Rs. 1,200 payable at the end of every six months is Rs. 40,000. If money is worth r% compounded semi-annually, then the value of r is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 6
The present value of a perpetuity of R paid at the end of every period is R/i, where i is the rate per period. Here the period is six months, so \(i = \frac{r}{200}\):
\( \displaystyle 40000 = \frac{1200}{i} \)
\( \displaystyle i = \frac{1200}{40000} = 0.03 \)
So the rate is 3% per half-year, which is a nominal rate of 6% per annum compounded semi-annually:
\( \displaystyle \frac{r}{200} = 0.03 \)
\(r = 6\)
Why the other options are incorrect
Option (2) 0.6 — Incorrect. Then i = 0.003 and the present value would be 1200/0.003 = Rs. 4,00,000.
Option (3) 0.006 — Incorrect. Then i = 0.00003 and the present value would be Rs. 4,00,00,000.
Option (4) 3 — Incorrect. 3% is the rate per half-year; r is the annual nominal rate, twice that.
CBSE Applied Mathematics (Class XII):
Perpetuity
