Calculate CAGR from the following data: Year — 2015, 2016, 2017, 2018; Revenue (₹) — 3,00,000, 3,50,000, 4,00,000, 4,50,000.

Question

Accepted Answer

> [!TLDR]
> CAGR measures the smoothed annual growth rate over a multi-year period. For revenues of ₹3,00,000 (2015) to ₹4,50,000 (2018), the CAGR is approximately **14.47%**.

The Compound Annual Growth Rate (CAGR) is the rate at which an investment or revenue would have grown if it had increased at a steady, compounded rate each year. It smooths out the actual year-to-year fluctuations and gives a single, comparable growth figure.

Why use CAGR? Because simple average growth can be misleading when numbers compound. For example, a 50% drop followed by a 100% gain averages to 25%, but the actual return is 0%. CAGR captures the true geometric growth.

The formula is:

> [!FORMULA]
> $$ 	ext{CAGR} = \left( \frac{	ext{Ending Value}}{	ext{Beginning Value}} ight)^{\frac{1}{n}} - 1 $$
> where $n$ is the number of years between the beginning and ending values.

Here, the beginning value is the revenue in 2015 (₹3,00,000) and the ending value is the revenue in 2018 (₹4,50,000). The number of years, $n$, is 2018 − 2015 = 3 years. Notice that we count the *intervals* between years, not the number of data points.

Let’s work through it step by step.

1. **Identify the beginning and ending values.**  
   Beginning Value (2015) = ₹3,00,000  
   Ending Value (2018) = ₹4,50,000

2. **Determine the number of periods.**  
   From 2015 to 2018 is 3 years. So $n = 3$.

3. **Set up the CAGR formula.**  
   $$ 	ext{CAGR} = \left( \frac{4,50,000}{3,00,000} ight)^{\frac{1}{3}} - 1 $$

4. **Simplify the fraction.**  
   $$ \frac{4,50,000}{3,00,000} = 1.5 $$

5. **Take the cube root.**  
   We need $1.5^{1/3}$. You can compute this using a calculator or by estimation.  
   $1.14^3 = 1.14 	imes 1.14 	imes 1.14 = 1.2996 	imes 1.14 \approx 1.4815$ (a bit low)  
   $1.145^3 = 1.145 	imes 1.145 	imes 1.145 \approx 1.311 	imes 1.145 \approx 1.501$ (slightly high)  
   So the cube root is about 1.1447. …

Q.Calculate CAGR from the following data: Year — 2015, 2016, 2017, 2018; Revenue (₹) — 3,00,000, 3,50,000, 4,00,000, 4,50,000.

Concept understanding — Compound Annual Growth Rate

Compound Annual Growth Rate (CAGR)

The Intuition First

The Precise Statement

Applying It to Our Example

Why CAGR Matters in Exams

Step 1 — identify endpoints and periods

Step 2 — apply the CAGR formula

Step 3 — evaluate

Step 1 — CAGR formula

Step 2 — Compute the growth ratio

Step 3 — Take the 5th root

Step 1 — Form the growth ratio

Step 2 — Apply the CAGR formula

Step 3 — Subtract 1

Step 1 — Write the CAGR relation

Step 2 — Take logarithms

Step 3 — Compute

Step 1 — Set up the CAGR relation

Step 2 — Halve the exponent

Step 3 — Match the given value

Step 1 — Use only the endpoints

Step 2 — Apply the CAGR formula

Step 3 — Compute

Step 1 — Identify begin, end and n

Step 2 — Substitute

Step 3 — Evaluate the fourth root

Q.Calculate CAGR from the following data: Year — 2015, 2016, 2017, 2018; Revenue (₹) — 3,00,000, 3,50,000, 4,00,000, 4,50,000.

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