Consider an investment of Rs. 15,000 whose annual values are given below:
| June 1, 2022 | June 1, 2023 | June 1, 2024 | June 1, 2025 |
| Rs. 15,000 | Rs. 16,500 | Rs. 19,800 | Rs. 20,790 |
then the CAGR % is: (given \( (1.386)^{1/3}=1.115 \))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 11.5%
CAGR uses only the beginning value, the ending value and the number of years n between them; the values in between do not matter. From June 1, 2022 to June 1, 2025, n = 3.
\( \displaystyle \text{CAGR}=\left(\frac{\text{Ending value}}{\text{Beginning value}}\right)^{1/n}-1 \)
\( \displaystyle \frac{20790}{15000}=1.386 \)
\( \displaystyle \text{CAGR}=(1.386)^{1/3}-1 \)
\( \displaystyle =1.115-1=0.115 \)
So the CAGR is 11.5%.
Why the other options are incorrect
Option (1) 11.15% — Incorrect. 11.15% misreads 1.115 − 1 = 0.115 as 0.1115.
Option (3) 23% — Incorrect. The rate is 11.5%, not 23%.
Option (4) 5.75% — Incorrect. The rate is 11.5%, not 5.75%.
CBSE Applied Mathematics (Class XII):
Compound Annual Growth Rate
