An investment of Rs. 40,000 grows to Rs. 57,600 in 2 years. Which of the following are correct?
(A) The total growth of the investment over the 2 years is 44%.
(B) The compound annual growth rate (CAGR) of the investment is 20%.
(C) The average annual growth rate, found by dividing the total growth by the number of years, is 22%.
(D) The CAGR of the investment is more than its average annual growth rate.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (B) and (C) only
The total growth is
\( \displaystyle \frac{57600 - 40000}{40000} \times 100 = \frac{17600}{40000} \times 100 = 44\% \)
The compound annual growth rate, with n = 2, is
\( \displaystyle \mathrm{CAGR} = \left[\left(\frac{57600}{40000}\right)^{1/2} - 1\right] \times 100 \)
\(= (\sqrt{1.44} - 1) \times 100 = (1.2 - 1) \times 100 = 20\%\)
The average annual growth rate divides the total growth by the number of years:
\( \displaystyle \frac{44\%}{2} = 22\% \)
So the total growth is 44%, the CAGR is 20% and the average annual growth rate is 22%.
Checking the statements
(A) The total growth of the investment over the 2 years is 44%. — Correct. 17600 ÷ 40000 = 0.44.
(B) The compound annual growth rate (CAGR) of the investment is 20%. — Correct. \(40000 \times (1.2)^2 = 57600\).
(C) The average annual growth rate, found by dividing the total growth by the number of years, is 22%. — Correct. 44% ÷ 2 = 22%.
(D) The CAGR of the investment is more than its average annual growth rate. — Incorrect. 20% is less than 22%; the simple average ignores compounding and inflates the yearly rate.