This TI-84 Online Calculator focuses on the Compound Annual Growth Rate (CAGR), a key financial metric for measuring the smooth, geometric return of an investment over multiple periods. Use the form below to quickly calculate your investment performance.
TI-84 Online Calculator: Compound Annual Growth Rate (CAGR)
TI-84 Online Calculator: CAGR Formula
$$CAGR = \left( \frac{\text{End Value}}{\text{Start Value}} \right)^{\frac{1}{\text{Years}}} – 1$$
Formula Source: Investopedia – CAGR | Corporate Finance InstituteVariables
- Start Value (P): The initial investment amount or value of the asset at the beginning of the period.
- End Value (F): The final investment amount or value of the asset at the end of the period.
- Number of Years (t): The length of the investment period in years.
- Annualized Return (CAGR): The calculated geometric mean of annual growth rates, expressing the return over the period.
Related Calculators
- Future Value Calculator
- Present Value Calculator
- Simple Interest Calculator
- Discounted Cash Flow (DCF) Calculator
What is Compound Annual Growth Rate (CAGR)?
CAGR is defined as the mean annual growth rate of an investment over a specified period of time longer than one year. It’s a fundamental concept frequently used in financial analysis and investment planning, providing a smoothed rate of return. Unlike simple arithmetic returns, CAGR takes the compounding effect into account, giving a more accurate picture of investment performance.
The value derived from this TI-84 online calculator helps investors compare the growth rate of different investment types or analyze historical returns of a single asset without the volatility of annual fluctuations. It assumes the profits are reinvested at the end of each period, thus providing a conservative and realistic assessment of growth potential.
How to Calculate CAGR (Example)
- Determine the Inputs: Identify the Start Value (P), End Value (F), and the number of Years (t). For example, P = $10,000, F = $18,000, t = 5 years.
- Calculate the Total Growth Ratio: Divide the End Value by the Start Value: $18,000 / $10,000 = 1.8$.
- Calculate the Exponent: Determine the reciprocal of the number of years: $1 / 5 = 0.2$.
- Apply the Exponent: Raise the growth ratio to the power of the exponent: $1.8^{0.2} \approx 1.1246$.
- Subtract One: Subtract 1 from the result to get the rate as a decimal: $1.1246 – 1 = 0.1246$.
- Convert to Percentage: Multiply by 100 to get the final CAGR percentage: $0.1246 \times 100 = 12.46\%$.
Frequently Asked Questions (FAQ)
Is CAGR a real annual rate?
CAGR is a geometric mean that represents a hypothetical, constant rate of return. It smoothens out volatility and does not reflect actual year-to-year returns, but it is the best measure for comparing performance over time.
What if the Start Value is zero?
If the Start Value is zero, the division by zero is mathematically undefined. The calculator will return an error, as CAGR can only be calculated for investments with a positive initial value.
Can the CAGR be negative?
Yes, if the End Value is less than the Start Value (i.e., the investment lost money over the period), the calculated CAGR will be a negative percentage.
How is CAGR different from IRR?
The Internal Rate of Return (IRR) is used when there are multiple cash flows (deposits and withdrawals) over the investment period. CAGR is a simpler calculation used when only the beginning and ending values are known.