If an investment value gets doubled in 10 years then its compound annual growth rate (CAGR) is: (Given \(2^{1/10} = 1.0729\))
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 7.29%
The CAGR r is the constant yearly rate that takes the beginning value V to the ending value in n years:
\(V(1 + r)^{10} = 2V\)
\(1 + r = 2^{1/10} = 1.0729\)
\(r = 0.0729 = 7.29\%\)
Why the other options are incorrect
Option (1) 5% — Incorrect. \((1.05)^{10} \approx 1.63\), so the value would not double in 10 years.
Option (2) 10% — Incorrect. 10% a year doubles the value in 10 years only at simple interest; compounded, \((1.10)^{10} \approx 2.59\).
Option (3) 12% — Incorrect. \((1.12)^{10} \approx 3.11\), far more than double.
CBSE Applied Mathematics (Class XII):
Compound Annual Growth Rate
