Q.At what rate percent per annum, compounded annually, will ₹6,250 amount to ₹7,290 in 2 years?

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.

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.

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.

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.

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.

Key Properties to Remember

1. CAGR is always ≤ arithmetic mean of yearly returns (unless all yearly returns are equal).
2. CAGR can be negative if the ending value is less than the beginning value.
3. CAGR assumes reinvestment of profits at the same rate — this is its fundamental assumption.
4. CAGR does not account for risk — two investments with the same CAGR can have very different volatility.

Final Answer

CAGR is the geometric average growth rate that describes how an investment would have grown if it grew at a steady, constant rate each year. It is calculated as:

where $n$ is the number of years. It smooths out volatility and gives the true annualised return, making it the standard metric for comparing investment performance over time.