CA Foundation · Quantitative Aptitude · Mathematics of Finance
The sales of Kavya Foods grew from ₹4,00,000 to ₹6,76,000 in 2 years. Assuming growth is compounded annually, what is the compound annual growth rate (CAGR)?
The CAGR is 30%. Sales rose by a factor of 6,76,000/4,00,000 = 1.69 over two years. Taking the square root gives 1.3 per year, meaning 30% annual compound growth. Checking: 4,00,000 × 1.3 × 1.3 equals ₹6,76,000.
- A30%Correct
- B38%
- C35%
- D25%
Explanation
CAGR = (6,76,000/4,00,000)^(1/2) - 1 = (1.69)^(1/2) - 1 = 1.3 - 1 = 30%. Check: 4,00,000 × 1.3 × 1.3 = 6,76,000. The 38% option is the simple average growth rate from total growth of 69% divided by 2 rounded wrongly, which ignores compounding (69%/2 = 34.5%, so it is not valid).
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