Our Annualized Return Calculator allows you to compute the average annual return, a crucial metric for investors to assess the performance of their investments over a specific period and compare various investment opportunities.

Use this calculator to make informed investment decisions or to better understand your portfolio’s performance.

## Annualized Return Calculator

**The calculator offers two calculation methods:**

**Calculation based on initial and final capital:**Ideal when you know the initial and final value of your investment as well as the investment duration. This method accounts for the compound interest effect and provides an accurate overview of the average annual appreciation.**Calculation based on individual yearly returns:**Perfect when you know the annual returns of your investment. You can input any number of annual returns – whether for two, five, or ten years. The calculator determines the geometrically averaged annual return, which takes into account fluctuations in individual years.

## Calculating the Average Annual Return

### 1. Method: Calculation with Initial and Final Value

This method is used when you know the initial value of your investment, the final value, and the investment duration.

**The formula is:**

\)

**Where:**

- r = average annual return
- E = final value of the investment
- A = initial value of the investment
- n = number of years

This formula takes into account the compound interest effect and gives you the geometrically averaged annual return.

#### Example:

Suppose you invest $10,000 and after 5 years your investment is worth $14,000.

\( r = \sqrt[5]{\frac{14000}{10000}} – 1 = 1.0695 – 1 = 0.0695 = 6.95\%\)

The average annual return is thus 6.95%.

### 2. Method: Calculation with Annual Returns

This method is used when you know the returns for individual years.

**The formula is:**

\)

**Where:**

- r = average annual return
- r
_{1}, r_{2}, …, r_{n}= returns of individual years - n = number of years

This formula calculates the geometric mean of the annual returns.

#### Example:

Suppose you have the following annual returns: 5%, -2%, 7%, 3%

\( r = \sqrt[4]{(1 + 0.05)(1 – 0.02)(1 + 0.07)(1 + 0.03)} – 1 = 1.0323 – 1 = 0.0323 = 3.23\%\)

The average annual return is thus 3.23%.

### Why Use the Geometric Mean?

The geometric mean is used because it takes into account the effects of compound interest and provides a more accurate representation of returns over time than the arithmetic mean. For comparison, the arithmetic mean of the above returns would be (5% – 2% + 7% + 3%) / 4 = 3.25%, which slightly overestimates the actual return.

Using the geometric mean ensures that negative returns are appropriately weighted and provides a more accurate picture of overall performance over the period under consideration.