**The Formula of Annualized Rate of Return Calculation (Table of Contents)**

## What is the Annualized Rate of Return Formula?

The term“annualized rate of return formula” refers to the formula which is used as the measure for calculation of the equivalent annual return that an investor receives from his investment over the given period of time. It considers the compound interest on the amount over the period of time.

An annualized rate of return is evaluated as an equivalent amount of annual return an investor is entitled to receive over a stipulated period of time. It is computed on the basis of time-weight and these are scaled down to a period of twelve months and this allows investors to compare the return on assets over a particular period of time.

The formula for calculation of the annualized rate of return is mathematically represented as below:

**Annualized Rate of Return Formula = ((P + G) / P) ^ (1 / n) – 1**

Here,

- P = principal amount or initial investment amount
- n = number of years
- G = gains or losses which is calculated by deducting the initial investment amount from the amount received at the end or on maturity.

### Explanation of the Annualized Rate of Return Formula

The annualized rate of return formula in excel can be derived by using the following steps:

**Step 1:** Firstly, determine the gains or losses which are calculated by deducting the initial investment amount from the amount received at the end or on maturity.

**Gains or losses = Amount received at the end – initial investment amount**

**Step 2:** Finally, the annualized rate of return formula in excel is expressed as shown below.

**Annualized Rate of Return = ((P + G) / P) ^ (1 / n) – 1**

### Examples of Annualized Rate of Return Formula

Given below are the examples of the annualized rate of return formula to understand it better.

#### Example #1

**Let us take the example of an investor who has invested an amount of $700,000 4 years back. At the end of 4 years, he received $1,000,000. What is the annualized rate of return of the investor?**

Given,

- Principal amount or initial investment amount (P) = $700,000
- Amount received at the end of the period = $1,000,000
- Number of years (n) = 4 years

Now, gains or losses (G) can be calculated using below formula as,

Gains or Losses (G) = Amount Received at the End – Initial Investment Amount

- = $1,000,000 – $700,000
**= $300,000**

Now, the annualized rate of return for the investor can be calculated as follows,

- = (($700,000 + $300,000) / $700,000) ^ (1 / 4) – 1

Annualized Rate of Return will be –

**Annualized Rate of Return = 9.33%**

Therefore, the annualized rate of return of the investor is 9.33%.

#### Example #2

**Let us take another example of a company that decides to invest an amount of $15,000,000 in a mutual fund. After a period of 10 years, the company receives $25,000,000. What is the total amount of gain or loss received by the company and its annualized rate of return?**

Given,

- Principal amount or initial investment amount (P) = $15,000,000
- Amount received at the end of the period = $25,000,000
- Number of years (n) = 10 years

Now, gains or losses (G) can be calculated as,

Gains or losses (G) = Amount Received at the End – Initial Investment Amount

- = $25,000,000 – $15,000,000
**= $10,000,000**

Now, the annualized rate of return for the investor can be calculated as follows,

- = (($15,000,000+ $10,000,000) / $15,000,000) ^ (1 / 10) – 1

Annualized Rate of Return will be –

**Annualized Rate of Return = 5.24%**

Therefore, the total amount of gain or loss received by the company after the period of 10 years is $10,000,000 with the annualized rate of return of 5.24%.

#### Example #3

**Let us take another example of a company that decides to invest an amount of $300,000 in a mutual fund. After a period of 2 years, the company receives $200,000. What is the annualized rate of return?**

Given,

- Principal amount or initial investment amount (P) = $300,000
- The amount received at the end of the period = $200,000
- Number of years (n) = 2 years

Now, in this case, the amount received at the end is less than the initial amount of investment, so there is a loss to the company that will be calculated as follows,

Gains or Losses (G) = Amount Received at the End – Initial Investment Amount

- = $200,000 – $300,000
**= -$100,000**

Now, the annualized rate of return for the investor can be calculated as below,

- = (($300,000 – $100,000) / $300,000) ^ (1 / 2) – 1

**Annualized Rate of Return = -18.35%**

Therefore, the annualized rate of return of the company in the present case from investing in a mutual fund is -18.35%.

### Relevance and Uses

The annualized rate of return formula in excel is an important concept used for measuring the annual growth rate of the investor over the period of time as it is one among the most accurate ways used for the determination of the returns earned by the investor on his individual assets, portfolios, etc. It helps the person to know the performance of the investment in the past and expected the performance of the investment in the future, thereby helping in making the informed decision.

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