Match the LIST-I with LIST-II
| LIST-I | LIST-II | ||
| A. | The present value of a perpetuity of Rs. 3120 payable at the beginning of each year, if money is worth 6 % effective. | I. | Rs. 2,00,000 |
| B. | The present value of a perpetuity of Rs. 5,000 payable at the end of each year, if money is worth 5 % compounded annually | II. | Rs. 1,50,000 |
| C. | The present value of a sequence of payments of Rs. 3,000 payable at the end of each 6 months and continuing forever, if money is worth 4 % compounded semi-annually. | III. | Rs. 1,00,000 |
| D. | The present value of a perpetuity of Rs. 3,000 payable at the end of each quarter, if money is worth 6 % compounded quarterly | IV. | Rs. 55,120 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A-IV, B-III, C-II, D-I
For a perpetuity of R per period at rate i per period, \( PV=\frac{R}{i} \) when payments are made at the end of each period, and \( PV=R+\frac{R}{i} \) when they are made at the beginning (perpetuity due). The rate i is always the rate per payment period.
A. The present value of a perpetuity of Rs. 3120 payable at the beginning of each year, if money is worth 6 % effective.
This matches IV. Rs. 55,120.
\( \displaystyle PV=3120+\frac{3120}{0.06} \)
\( \displaystyle =3120+52000 \)
\( \displaystyle =55120 \)
B. The present value of a perpetuity of Rs. 5,000 payable at the end of each year, if money is worth 5 % compounded annually
This matches III. Rs. 1,00,000.
\( \displaystyle PV=\frac{5000}{0.05}=100000 \)
C. The present value of a sequence of payments of Rs. 3,000 payable at the end of each 6 months and continuing forever, if money is worth 4 % compounded semi-annually.
This matches II. Rs. 1,50,000.
Rate per half-year: i = 4% ÷ 2 = 2% = 0.02.
\( \displaystyle PV=\frac{3000}{0.02}=150000 \)
D. The present value of a perpetuity of Rs. 3,000 payable at the end of each quarter, if money is worth 6 % compounded quarterly
This matches I. Rs. 2,00,000.
Rate per quarter: i = 6% ÷ 4 = 1.5% = 0.015.
\( \displaystyle PV=\frac{3000}{0.015}=200000 \)
So the matching is A-IV, B-III, C-II, D-I.
CBSE Applied Mathematics (Class XII):
Perpetuity
