Choose the correct statement about CAGR (compound annual growth rate)?

The correct answer is Option (4) → CAGR is calculated by using the final and beginning value of an investment.

Note: The given answer is as per the official NTA Answer Key. However, more than one answer is possible: Option (1) and Option (4) are both correct, as explained below.

The compound annual growth rate is the single yearly rate at which an investment would grow from its beginning value to its ending value if the gains were compounded every year:

    \( \displaystyle \text{CAGR} = \left[\left(\frac{EV}{SV}\right)^{1/n} - 1\right] \times 100 \)

where SV is the starting (beginning) value, EV the ending value and n the number of years.

Option (1) CAGR is the average annualized return of an investment. — Should also be correct, though not the answer given by NTA. CAGR replaces the uneven year-by-year returns by one steady yearly return giving the same final value, so it is the average annual return of the investment (a compound, not an arithmetic, average).

Option (2) CAGR is calculated by taking arithmetic mean of series of returns. — Incorrect. A gain of 50% followed by a loss of 50% has arithmetic mean 0%, but Rs.100 becomes Rs.150 and then Rs.75, a loss; the CAGR, \(\left(\frac{75}{100}\right)^{1/2} - 1 \approx -13.4\%\), shows this.

Option (3) CAGR is linear measure that does not account for the effects of compounding. — Incorrect. CAGR assumes the gains are reinvested every year; the power \(\frac{1}{n}\) in the formula is what accounts for compounding.

Option (4) CAGR is calculated by using the final and beginning value of an investment. — Correct. The formula uses only the ending value, the beginning value and the number of years.

Advice for the exam: When more than one option is correct, mark the most specific one, here Option (4), which states exactly how CAGR is calculated. If NTA’s provisional answer key marks a different option, challenge it during the answer-key challenge window, giving proper reasoning. NTA does revise its key when a challenge is well justified, so a sound challenge can raise your marks.