Match List-I with List-II
| List-I (Investment) | List-II (CAGR) | ||
| (A) | Rs. 40,000 grows to Rs. 48,400 in 2 years | (I) | 25% |
| (B) | Rs. 50,000 grows to Rs. 72,000 in 2 years | (II) | 50% |
| (C) | Rs. 64,000 grows to Rs. 1,25,000 in 3 years | (III) | 10% |
| (D) | Rs. 8,000 grows to Rs. 27,000 in 3 years | (IV) | 20% |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
The CAGR is found from \(\displaystyle\left(\frac{\text{EV}}{\text{SV}}\right)^{1/n} - 1\), so each ratio is written as a power with n equal to the number of years.
(A) Rs. 40,000 to Rs. 48,400 in 2 years
This matches (III) 10%.
\( \displaystyle \frac{48400}{40000} = 1.21 = (1.1)^2 \)
(B) Rs. 50,000 to Rs. 72,000 in 2 years
This matches (IV) 20%.
\( \displaystyle \frac{72000}{50000} = 1.44 = (1.2)^2 \)
(C) Rs. 64,000 to Rs. 1,25,000 in 3 years
This matches (I) 25%.
\( \displaystyle \frac{125000}{64000} = \frac{125}{64} = \left(\frac{5}{4}\right)^3 = (1.25)^3 \)
(D) Rs. 8,000 to Rs. 27,000 in 3 years
This matches (II) 50%.
\( \displaystyle \frac{27000}{8000} = \frac{27}{8} = \left(\frac{3}{2}\right)^3 = (1.5)^3 \)