What is a CAGR Calculator?
A CAGR Calculator (Compound Annual Growth Rate Calculator) enables investors to measure the true annualized return of an investment across multi-year holding periods.
Financial markets (stocks, mutual funds, real estate, gold) experience volatile year-to-year swings. CAGR smooths out annual fluctuations to provide a single, constant annual growth rate that makes disparate investments directly comparable.
The CAGR Calculation Formula
The Compound Annual Growth Rate (CAGR) formula is:
$$\text{CAGR (%)} = \left[ \left(\frac{\text{Final Value}}{\text{Initial Value}}\right)^{\frac{1}{n}} - 1 \right] \times 100$$
Where:
- Final Value ($FV$): Current or final value of the investment.
- Initial Value ($IV$): Original purchase or investment cost.
- $n$ (Years): Holding period in years.
Practical Worked Example: Stock Investment
Suppose you bought shares of an equity fund for ₹1,00,000 (₹1 Lakh) and sold them 5 years later for ₹2,50,000 (₹2.5 Lakhs):
- Initial Investment ($IV$): ₹1,00,000
- Final Value ($FV$): ₹2,50,000
- Holding Period ($n$): 5 Years
- Absolute Gain: $₹2,50,000 - ₹1,00,000 = \mathbf{₹1,50,000\text{ (150% Absolute Gain)}}$
- CAGR Calculation: $$\text{CAGR} = \left[ \left(\frac{250000}{100000}\right)^{\frac{1}{5}} - 1 \right] \times 100 = \left[ (2.5)^{0.2} - 1 \right] \times 100 = \mathbf{20.11% \text{ p.a.}}$$
Even though your investment gained 150% in absolute terms, your true annualized compound growth rate was 20.11% per year.
CAGR vs. Absolute Return Comparison
| Metric | Absolute Return | CAGR (Annualized Growth) |
|---|---|---|
| Formula | $\frac{FV - IV}{IV} \times 100$ | $[(\frac{FV}{IV})^{\frac{1}{n}} - 1] \times 100$ |
| Accounts for Time? | No | Yes |
| Best Used For | Investments under 1 year | Investments over 1 to 40+ years |
| Example (₹1L to ₹2L in 10 Yrs) | 100% Total Gain | 7.18% Annualized CAGR |