Mr. X invested Rs. 4,00,000 in shares for 5 years. The value of this investment was Rs. 4,50,000 at the end of the second year, Rs. 4,90,000 at the end of the third year and on maturity, the final value stood at Rs. 6,00,000. The compound annual growth rate of this investment is:
[Given that: \((1.5)^{1/5} = 1.084\)]
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 8.4 %
The compound annual growth rate uses only the beginning value \(V_0\), the final value \(V_n\) and the number of years n:
\( \displaystyle \text{CAGR} = \left(\frac{V_n}{V_0}\right)^{1/n} - 1 \)
\( \displaystyle \text{CAGR} = \left(\frac{600000}{400000}\right)^{1/5} - 1 = (1.5)^{1/5} - 1 \)
\(\text{CAGR} = 1.084 - 1 = 0.084 = 8.4\%\)
The values at the end of the second and third years do not enter the CAGR.
CBSE Applied Mathematics (Class XII):
Compound Annual Growth Rate
