A certified financial analyst ensuring the accuracy of our calculation methodologies.
This calculator determines the difference between the Compound Annual Growth Rate (CAGR) and the Simple Annual Return (SAR) on an investment, providing clarity on the true effect of compounding over time.
CAGR vs. Simple Annual Return Calculator
CAGR vs. Simple Return Formula
Compound Annual Growth Rate (CAGR):
$$ \text{CAGR} = \left( \frac{\text{Final Value}}{\text{Initial Value}} \right)^{\frac{1}{\text{N}}} – 1 $$
Simple Annual Return (SAR):
$$ \text{SAR} = \frac{\left( \frac{\text{Final Value} – \text{Initial Value}}{\text{Initial Value}} \right)}{\text{N}} $$
Formula Source: Investopedia (CAGR) Formula Source: The Balance (Simple Return)Variables Explained
- Initial Value (V): The starting market value or principal investment amount.
- Final Value (F): The ending market value of the investment after N years.
- Number of Years (N): The investment period in years. This must be a positive number.
Related Financial Calculators
- Present Value Calculator (Low Competition Keyword)
- Future Value of Annuity Calculator (Low Competition Keyword)
- Monthly Investment Return Calculator (Low Competition Keyword)
- Effective Annual Rate (EAR) Tool (Low Competition Keyword)
What is Compound vs. Simple Return?
The difference between compound and simple returns is fundamental to understanding investment performance, especially over long periods. The Simple Annual Return (SAR), also known as the arithmetic mean return, calculates the total gain or loss and distributes it evenly across the investment period without considering the growth of the return itself (compounding).
The Compound Annual Growth Rate (CAGR) is the geometric progression ratio that provides the constant annual rate of return over the specified period. It assumes that profits are reinvested each year, generating earnings on previous earnings. This rate is a more accurate representation of an investment’s true performance because it accounts for the power of compounding.
For any period longer than one year, the CAGR will typically be lower than the SAR unless the returns are perfectly consistent or the investment had losses, making the CAGR the preferred metric for comparison across different investments.
How to Calculate CAGR and SAR (Example)
Let’s use an example: An investment grows from $10,000 to $15,000 over 5 years.
- Calculate Total Return (TR): Divide the gain ($15,000 – $10,000 = $5,000) by the Initial Value ($10,000). TR = $5,000 / $10,000 = 0.50 (or 50%).
- Calculate Simple Annual Return (SAR): Divide the Total Return by the Number of Years. SAR = 50% / 5 Years = 10.00%.
- Calculate CAGR: Divide the Final Value by the Initial Value ($15,000 / $10,000 = 1.5).
- Apply the Time Exponent: Raise the result from Step 3 to the power of (1 / 5 Years), which is $1.5^{0.2} \approx 1.08447$.
- Final CAGR: Subtract 1 from the result: $1.08447 – 1 = 0.08447$, or 8.45%.
In this example, the Simple Annual Return (10.00%) significantly overstates the true compound performance (8.45%).
Frequently Asked Questions (FAQ)
What is the main advantage of CAGR?
CAGR smooths out volatile returns and provides a more realistic measure of the average annual growth rate, as it accounts for the compounding effect.
When is Simple Annual Return (SAR) useful?
SAR is easier to calculate and is typically used for short-term investments (less than a year) or as a quick, rough estimate of performance before considering compounding.
Does CAGR account for deposits or withdrawals?
No, the basic CAGR formula treats the entire investment as a single lump sum that grows from V to F. For investments with intermediate contributions, you should use the Modified Dietz Method or Time-Weighted Rate of Return (TWR).
Why is my CAGR lower than my SAR?
When returns are positive, the CAGR is mathematically guaranteed to be lower than the SAR for periods longer than one year. This is because SAR calculates the arithmetic mean, while CAGR calculates the geometric mean, which accounts for the dampened effect of compounding on successive annual returns.