Consider the value of an investment in the given years. (Given \( (1.518)^{1/3}=1.149 \))
| 1 Jan 2020 | 1 Jan 2021 | 1 Jan 2022 | 1 Jan 2023 |
| Rs. 10000 | Rs. 12000 | Rs. 13800 | Rs. 15180 |
(A) The year-to-year growth rate of investment in 2021-2022 is 20%.
(B) The year-to-year growth rate of investment in 2022-2023 is 10%.
(C) The compound annual growth rate (CAGR) percentage is 11.49%
(D) The compound annual growth rate (CAGR) percentage is 14.9%
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B) and (D) only
Year-to-year growth rate = \( \frac{\text{new value}-\text{old value}}{\text{old value}}\times 100 \).
\( \displaystyle 2020\text{-}2021:\ \frac{12000-10000}{10000}\times 100=20\% \)
\( \displaystyle 2021\text{-}2022:\ \frac{13800-12000}{12000}\times 100=15\% \)
\( \displaystyle 2022\text{-}2023:\ \frac{15180-13800}{13800}\times 100=10\% \)
CAGR over the n = 3 years from 1 Jan 2020 to 1 Jan 2023:
\( \displaystyle \text{CAGR}=\left(\frac{\text{final value}}{\text{initial value}}\right)^{1/n}-1 \)
\( \displaystyle =\left(\frac{15180}{10000}\right)^{1/3}-1 \)
\( \displaystyle =(1.518)^{1/3}-1 \)
\( \displaystyle =1.149-1=0.149=14.9\% \)
So the growth rate is 15% in 2021-2022 and 10% in 2022-2023, and the CAGR is 14.9%.
Checking the statements
(A) The year-to-year growth rate of investment in 2021-2022 is 20%. — Incorrect. It is 15%; 20% is the growth in 2020-2021.
(B) The year-to-year growth rate of investment in 2022-2023 is 10%. — Correct. It is 10%.
(C) The compound annual growth rate (CAGR) percentage is 11.49% — Incorrect. The CAGR is 14.9%, not 11.49%.
(D) The compound annual growth rate (CAGR) percentage is 14.9% — Correct. The CAGR is 14.9%.
Tip: Count the years for CAGR as the number of intervals, not the number of values: four dates give n = 3, which matches the cube root given in the question.