Calculator for Math Problems

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Module Reviewed and Validated By: David Chen, CFA. This calculator for math problems uses industry-standard formulas for financial analysis.

The Annualized Return Calculator helps you determine the effective compound annual growth rate (CAGR) of an investment over a specified period. It’s a crucial tool for financial analysts and investors to accurately compare the performance of different assets regardless of their investment timelines. Simply enter any three of the four variables to solve for the missing one.

Annualized Return Calculator

Calculation Steps:

Annualized Return Calculator Formula

Annualized Return (AR) = [ ( Final Value / Initial Investment ) ^ ( 1 / Years ) – 1 ] x 100

Source: Investopedia: Annualized Return Definition

Variables

The calculator uses the following four key variables, allowing you to solve for any one of them by entering the other three:

  • Initial Investment (P): The starting capital amount of the investment.
  • Final Value (F): The total value of the investment at the end of the period, including principal and accumulated earnings.
  • Number of Years (T): The total duration of the investment, expressed in years (or a fraction of a year).
  • Annualized Return (AR): The geometric average annual growth rate, expressed as a percentage.

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What is Annualized Return?

Annualized return is one of the most important metrics in finance for evaluating investment performance. It represents the compound rate of growth achieved by an investment over a given time period, usually longer than one year, expressed on a per-year basis. It provides a standardized figure that allows for an apples-to-apples comparison between investments held for different lengths of time.

Unlike a simple return, which only measures the total gain or loss, the annualized return accounts for the compounding effect. This means it smooths out the year-to-year volatility and shows what the average rate of growth was if the investment had grown consistently each year.

How to Calculate Annualized Return (Example)

Let’s find the Annualized Return (AR) if an Initial Investment (P) of $50,000 grew to a Final Value (F) of $80,000 over 7 years (T).

  1. Determine the Ratio: Divide the Final Value by the Initial Investment. ($80,000 / $50,000 = 1.6$)
  2. Determine the Fractional Exponent: Calculate $1/T$. ($1 / 7 \approx 0.142857$)
  3. Raise to the Power: Raise the ratio (1.6) to the fractional exponent (0.142857). ($1.6^{0.142857} \approx 1.0696$)
  4. Subtract One: Subtract 1 from the result to get the decimal return. ($1.0696 – 1 = 0.0696$)
  5. Convert to Percentage: Multiply by 100 to get the Annualized Return percentage. ($0.0696 \times 100 = 6.96\%$)

Frequently Asked Questions (FAQ)

What is the difference between Simple Return and Annualized Return?

Simple return measures the total gain/loss over the entire period, while annualized return converts that total return into an average compounded annual rate, making it better for long-term comparison.

Why must I enter 3 of the 4 variables?

The underlying formula for Annualized Return contains four variables (P, F, T, AR). In mathematics, you need to know the value of all but one variable to solve for the unknown one.

Can I use this for investments less than one year?

Yes, you can input a fraction of a year for T (e.g., 0.5 for six months). The calculator will still provide the compound annual rate based on that period’s performance.

Is Annualized Return the same as CAGR?

Yes, Annualized Return is often used interchangeably with Compound Annual Growth Rate (CAGR). They both refer to the geometric mean rate of return over a specified period.

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