Match List-I with List-II
| List-I (Perpetuity) | List-II (Present value) | ||
| (A) | Rs. 500 at the end of every half-year, money worth 10% p.a. compounded half-yearly | (I) | Rs. 12,500 |
| (B) | Rs. 500 at the end of every quarter, money worth 10% p.a. compounded quarterly | (II) | Rs. 10,000 |
| (C) | Rs. 500 at the end of every year, money worth 4% p.a. compounded annually | (III) | Rs. 10,500 |
| (D) | Rs. 500 at the beginning of every year, money worth 5% p.a. compounded annually | (IV) | Rs. 20,000 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
The present value of a perpetuity of R at the end of each period is \(\frac{R}{i}\), and at the beginning of each period it is \(R + \frac{R}{i}\), where i is the rate per period.
(A) Rs. 500 every half-year at 10% p.a. compounded half-yearly
This matches (II) Rs. 10,000.
\( \displaystyle i = 0.05,\quad P = \frac{500}{0.05} = 10000 \)
(B) Rs. 500 every quarter at 10% p.a. compounded quarterly
This matches (IV) Rs. 20,000.
\( \displaystyle i = 0.025,\quad P = \frac{500}{0.025} = 20000 \)
(C) Rs. 500 every year at 4% p.a.
This matches (I) Rs. 12,500.
\( \displaystyle i = 0.04,\quad P = \frac{500}{0.04} = 12500 \)
(D) Rs. 500 at the beginning of every year at 5% p.a.
This matches (III) Rs. 10,500.
\( \displaystyle P = 500 + \frac{500}{0.05} = 500 + 10000 = 10500 \)