Identify the formula used for List I from List II
| List-I | List-II | ||
| (A) | Present value of perpetuity payable at the end of each payment period | (I) | \( R+\displaystyle\frac{R}{i} \) { Rs. \( R \) payable at the beginning of each payment period, \( i \) = interest per rupee per payment period } |
| (B) | Present value of perpetuity payable at the beginning of each payment period | (II) | \( \left(\displaystyle\frac{V_{n}}{V_{0}}\right)^{1/n}-1 \), \( V_{n} \) = Final value of investment, \( V_{0} \) = Beginning value of the investment, \( n \) = number of years |
| (C) | Computation of CAGR | (III) | \( \displaystyle\frac{C-s}{n} \), \( C \) = Original cost, \( s \) = Scrap value, \( n \) = number of years |
| (D) | Annual Depreciation | (IV) | \( \displaystyle\frac{R}{i} \) { Rs. \( R \) payable at the end of each period, \( i \) = interest per rupee per payment period } |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) - (IV), (B) - (I), (C) - (II), (D) - (III)
(A) Present value of perpetuity payable at the end of each payment period
This matches (IV) \( \frac{R}{i} \) (an immediate perpetuity).
(B) Present value of perpetuity payable at the beginning of each payment period
This matches (I) \( R+\frac{R}{i} \): the first payment is made now, and the rest form an immediate perpetuity (a perpetuity due).
(C) Computation of CAGR
This matches (II) \( \left(\frac{V_{n}}{V_{0}}\right)^{1/n}-1 \), the compound annual growth rate from the beginning and final values over n years.
(D) Annual Depreciation
This matches (III) \( \frac{C-s}{n} \), the yearly depreciation under the straight line method.
So the matching is (A)-(IV), (B)-(I), (C)-(II), (D)-(III).