Which of the following is correct about the compound annual growth rate (CAGR)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → CAGR is calculated by the final and beginning value of an investment.
The compound annual growth rate is the constant yearly rate at which the beginning value would grow to the final value in n years, with compounding:
\( \displaystyle \text{CAGR} = \left(\frac{\text{Final value}}{\text{Beginning value}}\right)^{\frac{1}{n}} - 1 \)
It needs both the final and the beginning values.
Why the other options are incorrect
Option (1) CAGR is calculated by only the final value of an investment. — Incorrect. The formula also needs the beginning value.
Option (3) CAGR describes the effect of simple interest. — Incorrect. CAGR assumes growth is compounded every year.
Option (4) CAGR is calculated by taking arithmetic mean of series of returns. — Incorrect. CAGR is a geometric (compound) average of the yearly growth; the arithmetic mean of the returns ignores compounding.
CBSE Applied Mathematics (Class XII):
Compound Annual Growth Rate
