Q.An investment's starting value is ₹ 10,000 and it grows to ₹ 60,000 in 4 years. The CAGR is : (Given : 61/4=1.56508) (A) 1.56% (B) 5.65% (C) 15.65% (D) 56.50%
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🔒 Start your 14-day free trial to unlock the full solution →Concept understanding — Compound Annual Growth Rate
Compound Annual Growth Rate (CAGR)
The Intuition First
Imagine you put ₹100 into a business. After one year, it grows to ₹120. After two years, it becomes ₹150. After three years, it's ₹200.
If someone asks, "What was the average yearly growth rate?", you might be tempted to say: "Year 1 grew 20%, Year 2 grew 25%, Year 3 grew 33.3% — so average is about 26%." But that's misleading. Why? Because each year's growth compounds on the previous year's base. You can't just average percentages that act on different starting amounts.
CAGR solves this problem. It answers: "If this investment had grown at a steady, constant rate every year, what would that rate be?" It smooths out the bumps and gives you one number that tells you the true annualised return.
CAGR is not the actual return in any single year. It's the geometric average — the rate that, if applied every year, would take you from the start value to the end value.
The Precise Statement
CAGR is the mean annual growth rate of an investment over a specified period longer than one year. It represents one of the most accurate ways to calculate and determine returns for anything that can rise or fall in value over time.
CAGR=(Beginning ValueEnding Value)n1−1
Where:
- Ending Value = final value of the investment
- Beginning Value = initial value of the investment
- n = number of years
Applying It to Our Example
Beginning Value = ₹100, Ending Value = ₹200, n = 3 years.
CAGR=(100200)31−1=(2)0.333−1≈1.26−1=0.26=26%
So the CAGR is 26%. Notice this is lower than the simple average of 26.1% we calculated earlier — that's because CAGR correctly accounts for the compounding effect.
A common mistake is to use the arithmetic mean of yearly returns. For example, if an investment goes up 50% one year and down 50% the next, the arithmetic mean is 0%, but you've actually lost money (₹100 → ₹150 → ₹75). CAGR correctly gives -13.4%.
Why CAGR Matters in Exams
In Indian competitive exams (CAT, GMAT, banking, SSC, UPSC), CAGR appears in:
- Data Interpretation: Tables showing company revenues or GDP over years — you'll need to compute CAGR quickly.
- Quantitative Aptitude: Direct formula-based questions.
- Finance/Investment: Comparing mutual fund or stock returns. …
CAGR $=\left(\dfrac{\text{final}}{\text{initial}}\right)^{1/n}-1=\left(\dfrac{60000}{10000}\right)^{1/4}-1=6^{1/4}-1=1.56508-1=0 …
(60000/10000)1/4−1=61/4−1=0.56508≈56.50%.
CAGR=(VinitialVfinal)1/n−1, where n = number of years.
- Ratio of values: 1000060000=6.
- Raise to 1/n=1/4: 61/4=1.56508 (given). …
- CBSE 2025Set 465/W1XZY/41 markMCQQ.The CAGR of an investment, whose starting value is ₹ 5,000 and it grows to ₹ 25,000 in 4 years, is : [Given (5)0.25=1.4953] (A) 49.53% (B) 14.95% (C) 495.3% (D) 1.49%
›Reveal solutionSolution
(500025000)1/4−1=50.25−1=1.4953−1=0.4953=49.53%.
CAGR=(ViVf)1/n−1, where Vi = initial value, Vf = final value, n = number of years.
- Find the growth ratio: ViVf=500025000=5 over n=4 years. …
- CBSE 2024Set 465/S/RQPS/41 markMCQQ.An investment's starting value is ₹ 10,000 and it grows to ₹ 60,000 in 4 years. The CAGR is : (Given : 61/4=1.56508) (A) 1.56% (B) 5.65% (C) 15.65% (D) 56.50%
›Reveal solutionSolution
(60000/10000)1/4−1=61/4−1=0.56508≈56.50%.
CAGR=(VinitialVfinal)1/n−1, where n = number of years.
- Ratio of values: 1000060000=6.
- Raise to 1/n=1/4: 61/4=1.56508 (given). …
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