Which of the following is correct about the compound annual growth ra…

The correct answer is Option (4) → It smoothens out the volatile nature of year by year growth/decay rates and provides more accurate results.

Note: The given answer is as per the official NTA Answer Key. However, Option (1) could also be a possible answer, as explained below.

For a beginning value \(V_0\) and an ending value \(V_n\) after n years:

    \( \displaystyle \text{CAGR} = \left(\frac{V_n}{V_0}\right)^{1/n} - 1 \)

It is the single constant yearly rate that, compounded each year, takes \(V_0\) to \(V_n\). It replaces uneven yearly rates by one steady rate.

Option (1) It is an average annualized return of an investment. — Should also be correct, though not the answer given by NTA. CAGR is the one steady yearly rate at which an investment would grow from its starting value to its final value. Finance books often describe this steady rate in exactly these words, as the “average annualised return”, so this description is also acceptable. It would be wrong only if “average” meant adding up the returns of each year and dividing by the number of years.

Option (2) It is calculated by taking the arithmetic mean of series of returns. — Incorrect. CAGR is a geometric mean of the yearly growth factors, \(1 + \text{CAGR} = \left[(1 + r_1)(1 + r_2)\cdots(1 + r_n)\right]^{1/n}\), not an arithmetic mean.

Option (3) It is a linear measure that does not account for the effects of compounding. — Incorrect. CAGR is built on compounding, so it is not a linear measure.

Option (4) It smoothens out the volatile nature of year by year growth/decay rates and provides more accurate results. — Correct. Using one steady rate is exactly what smooths out the year-by-year ups and downs.