# How to Convert Daily Returns to Annual

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The term daily return indicates the daily rate of growth of an investment. Since the majority of investments are reported as annual returns, it is important to convert your daily returns to annualized rates of return. To accomplish this, you need to go beyond simple mathematical calculations to determine compound growth. Just multiplying your daily return by ​365​ will not enable you to accurately annualize daily returns for all investments.

## Formula for Calculating the ARR

You can compute the annualized rate of return (ARR) on an investment by performing the following formulated steps:

1. Convert to a decimal number. Convert the daily return percentage to a decimal number by dividing this percentage by ​100​. For instance, if your investment returns ​0.02​ percent each day, dividing it by ​100​ will give your the decimal number of ​0.0002​.

2. Add the number ​1​. When you add the numeral "​1​" to the number calculated in Step ​1​, the resulting number will be ​1.0002​.

3. Raise to the power of ​365​. Next, raise the figure ​1.0002​ to the power of ​365​, which will give you the number ​1.0757​.

4. Subtract ​1​ from ​1.0757​. By subtracting ​1​ from the number ​1.0757​, you will have the annual return as a decimal number of ​0.0757​.

5. Multiply by ​100​. Convert the decimal number into a percentage form by multiplying ​0.0757​ by ​100​. This will determine that the annual return on your investment is ​7.57​ percent. You can annualize daily returns for additional investments in this same way.

## Annualize Daily Returns for Investments: Business Day System

Some investments that you own or would like to purchase may use a business day system. For these investments, you first need to determine the cumulative investment value at the beginning of the month you choose to use for your analysis. For an investment that you own, you can find the value of your account as printed on the latest statement from your broker.

For any investment that you want to purchase, you can locate daily data or month-to-date return reports on the investment company's website. Next, following the same procedure, locate the investment's end-of-month value.

## Total Monthly Return and Average Daily Rate of Return

Next, subtract the figure representing the end-of-month value from the beginning value figure. The resulting number equals the investment's total monthly return. To determine your average daily rate of return, divide the monthly average return by the number of days you want to examine. Next, convert this figure to a decimal number by dividing the average daily rate by ​100​, and then add the number ​1​ to the decimal number.

## Number of Days You Receive Returns During the Year

For investments using a business day system, find the number of days during the year that you receive returns. Typically, there are ​250​ days each year in the business day system. This number includes the number of regular business days in any ​12-month​ time period, excluding ​10​ federal holidays.

Of course, for investments that do not use a business day system, you will make your calculations using ​365​ days for the year. Consult your investment broker to ensure which daily return system your investment uses.

Take the decimal figure that resulted when you divided your average daily rate by ​100​ and added ​1​ above. This is the figure that you will raise to a power that corresponds to the number of days during the year when returns are posted for an investment.

Using either an online or offline scientific calculator, select the key that designates the letter "x" raised to the power of "y." For "x," enter the decimal figure, and for "y," use the number of days in your annual return system. Then, subtract the number ​1​ from the resulting figure. Next, multiply the resulting number by ​100​ to determine your annualized daily rate of return.

## How to Calculate Multi-Year Returns on Investments

The figure representing a multi-year return on an investment reveals the total profit over several years' time. For example, if your profits equal ​\$12,000​, ​\$13,000​ and ​\$15,000​ over three consecutive years, the multi-year profit total equals ​\$40,000​. If your initial investment was ​\$100,000​, divide ​\$40,000​ by ​\$100,000​. Then multiply this figure by ​100​ to determine your multi-year return of ​40 percent​.